This is just a bunch of semi-disjointed, miscellaneous tips that I have for people who might be looking for assistance on certain courses or in certain situations. It is not highly organized, nor is it comprehensive of every hint one could give about the game or every secret on every course. It is, however, provided in the hope that it proves helpful to at least one person.

Some elements are opinion, and some statements may be inconsistent with others' experiences. This is based solely on my own gameplay experience and what I've found to be optimal for me when playing. I don't consider myself to be any kind of authority on this game, but I do feel like I understand it well enough at this point to give others some assistance based on my experience.

I may or may not add more to this at a later time.

Enjoy, and I hope someone out there gets some good use out of this!

Special thanks to Zork Nemesis, who suggested a few additional tips and reminded me of a few I forgot the first time around.

Some general gameplay tips.

-Drift anywhere you can, and try to build your drift-boosts to level 3 when possible. A level 3 drift can work wonders! Also don't be afraid to fire off your level 3 boost as soon as you've got it - you can start drifting again and get a second one!
-That said, there are certain places where driving without drifting is a better idea, such as on straightaways (where boost builds extremely slowly due to having to avoid drifting into the corner) and during Traffic Attack challenges (where your control is limited beyond usefulness by drifting).
-Utilize drifting a lot during Ring Race challenges. The speed difference between braking for a corner and drifting through it will often be the difference between success and failure. You'd be surprised how well you can take certain corners in these challenges while drifting!
-Many ramps and transform gates throughout the game are high enough that you can perform two or even three stunts if you time it right.
-Start a stunt before entering a plane-to-boat or plane-to-car transform gate - as long as it finishes after you pass through the gate, it counts towards your Transform Boost. This means you can be 90% done with a flip upon hitting the gate and still get the boost for it!
-Aim for the very top of plane-to-car/plane-to-boat transform gates to get the most stunts possible before landing.
-Boost pads are your friend. Aim for them! They can even make geographically-longer routes faster than shorter alternate routes because of how much they boost your speed.
-Experiment with stunts at every opportunity to find the best and not-so-best places for them. There are a few places that I was quite surprised to learn were perfect for stunt-chaining, and others that I thought looked ideal for stunts but weren't in the end.
-When drifting in a car or boat, lining yourself up on jumps so that you are nearly perpendicular to the track and rolling towards the outside of your turn when jumping (think of the big stepped corner before the water section on Temple Trouble) will give you a nice extra lurch forward in addition to the boost upon landing.
-(Suggested by Zork Nemesis) While multi-flips and multi-rolls will get you a level 3 boost, mixing rolls and flips (2+ of one and at least 1 of the other) will get you a more powerful level 4 boost.

-At the first curve is a rather well-hidden shortcut. If you look closely at the outside of the curve (directly ahead of you as you approach), you'll notice that part of the guardrail is missing. If you drive off the track here while pulling to the left, you can cross a couple of square platforms and land on a narrow ramp leading back to the track. This will get you a slot machine token, a triple-boost pickup, and a nice stunt opportunity as you fly back onto the track.
-The route with the rollers is actually shorter than the route with the loop. There's very little reason to take the loop route over the roller route unless you have really bad luck with the rollers.
-You can perform rolls when dropping off of some of the platforms that lower into the water at the end of lap 2. It's tricky, but if you time it just right, you can get a roll in off each of the last three.
-The boat section in the final stretch is shorter and straighter than the car section, but the car section can be beneficial as it offers the opportunity to build up a big drift-boost. Which one is better will depend almost entirely on your driving style.

-Most of the ramps on this course are large enough to get at least 2 stunts in before landing. The transform gates may be exceptions, except for the first one, where you can get in at least 3 stunts if you time it right.
-The transform gate at the end of the first water section (going into the wild-west set) is one of the #1 offenders when it comes to the "trick buffering" bug - wherein the game "misses" your input to perform a stunt, but then executes it later when you try to do stunts again, leading to potentially unwanted stunts. The best solution is simply not to do stunts here, but if you do end up with a buffered trick, the water section's ramps are a good place to get rid of it.

-There aren't any real risk-boost opportunities on this flight-heavy course, so make the most of the air boosters throughout the track, as well as the early transform gate in the water section.
-Drift wide on the corner in the car section on the second ship, and you can hit all three boost pads.
-At the final curve, a Glove can help you bust through the boxes if you decide to take the inner turn. Otherwise, another racer going in before you can be useful to clear out the crates (while also losing momentum so you can pull ahead!).
-Adding onto the above, the AI has a tough time with those crates, meaning that on most difficulty settings you should still be able to come out ahead of them by taking the wider turn on the final corner.

-The higher road at the fork entering the cave during lap 1 isn't significantly faster than the lower one, and doesn't really have any benefits aside from a stunt opportunity and a slot token.
-Many of the waves kicked up during lap 2 aren't tall enough for stunts. The big one in the final stretch of water usually is, but if you're farther back in the back it may dissipate too quickly.
-Risk-boost like a maniac during lap 3! Pay attention though, as it's easy to get distracted and end up inadvertently flying off the course in that maze of canyons.

-The dip in the road before the big downhill with the monkey statues is big enough to pull off a roll if you're traveling at high speed. The drop at the bottom, however, is not big enough for stunts.
-The side paths at the three-way fork are substantially shorter than the center path, and also offer a chance at a big stunt jump and a super pickup (Ice x 6). The spots where the road dips down at the start of each path are, like the big ramp shortly before, big enough to execute a well-timed roll.
-Drifting tightly through the big turn before the water section and rolling towards the outside of the turn on the drops will get you quite a bit of extra speed.

-Memorize the locations of the boost pads on the road so as to maximize their effectiveness. If you're in first, watch out for the badniks that will attack you, but pay attention as their energy beams will frequently outline boost pads on the track.
-Drift a lot - this is a great course for it!
-The gold asteroids during the flight section are no good for risk-boosts (either that, or they're just really, really difficult to risk-boost with). The darker-colored asteroids, however, are very useful for risk boosts, especially the ring-shaped ones that you pass through.

-The second-to-last set of stairs immediately after the water section is large enough to pull off 2 stunts, as is the final set of stairs there.
-The dark sand in certain parts of this course will slow you down, so stay off it!
-During the big stair climb, the second landing is too short to perform stunts reliably. Unless you've got the timing perfect, it's faster to do one stunt on the first landing, skip the second, then perform a chain of stunts at the top of the stairs.
-Unless you want the super pickup, the alternate route in the final curve isn't that much better due to the numerous hard-to-dodge statues, especially since you can build a hefty drift-boost around the wider curve.

-(Suggested by Zork Nemesis) It's possible to cut the corner in the air when entering the flight section during lap 1 and save yourself a lot of time, especially for time trials. You won't get any items though.
-The land route at the end of laps 1 and 2 is MUCH longer than the water route. There is typically no benefit to using it.

-This is one of the best courses in the game for risk boosts. The hills in the first section are very effective, but be careful as certain ones have invisible collisions above/below them to keep you on the course.
-(Suggested by Zork Nemesis) Cutting through the hole in the tree on all three laps is usually the fastest way through the first flight section. Don't just wait until lap 3 when the orange rings lead to it!
-You can perform a lot of rolls to line yourself up with where you want to go during the water segment. The ramp off to the right is one of the best spots in the game for getting massive stunt-chains, especially since the stone pathway stretching over the track is non-solid, meaning you'll sail right through it.
-The large structure just before the finish has an insanely large collision box. Risk-boosting with it is not advisable because of this, unless you can find the true edges of its collision and memorize them.

-You can perform stunts at the two spots where the track abruptly goes downhill in the castle. You have to be quick, but you can get a single stunt in before hitting the ground.
-The water section only curves in one direction - right on the normal track, left on the mirror track. Memorize this, and you'll fare much better in the caverns where the next turn is rarely visible!
-The ramp that forms during lap 2 from a fallen stalactite in the caverns leads to a super pickup, but not much of a shortcut. The main route is easier, and the stunt opportunity offered by the alternate route can be counterproductive when coming into the final stretch.
-The final hairpin corner is one of the nastiest spots in the entire game, and is the reason many people hate this course. The trick, however, is not to perform stunts when going through the final transform gate. Instead, line yourself up to drift into the corner (holding your drift button in the air helps this, especially if you turn slightly in the direction of the corner). You can easily switch-drift to go into the nasty curve, then switch-drift again to enter the straightaway with a boost.

-Despite appearances, risk boosts are rather difficult on this course. Nonetheless, there are many opportunities to do them, including a lot of non-obvious ones. Experiment to find your favorite spots.
-The middle route during the forked portion of lap 2 offers more opportunities for stunts than the left or right routes. At the first two-way fork, you can take either of the routes, then move to the middle one on the wide platform before the track splits again.

-The stairs after the turn with the bouncy castle are much like the final transform gate on Chilly Castle: avoid doing stunts here and instead focus on lining up to land in a drift for the next corner. This is also an ideal place to slam on the brakes harder than you ordinarily would, as that next corner is very tight and hitting the far wall will slow you down a lot!
-Once the spiders are on their backs, they are non-solid, meaning you can drive through them.
-The barrels in the cellar during lap 3 alternate which side of the track they appear on. Keep to the side where a barrel has most recently passed, and you'll have no trouble with them.
-Most of the sudden drops in lap 3 are too small for stunts.
-The side route before the church in lap 3 is straighter, but it is also filled with headstones that are very hard to dodge. The normal route actually doesn't take significantly longer than the shortcut, especially if those who take the shortcut hit a headstone or two.

-The initial flight section is another great risk-boosting opportunity, although it can be quite a bit tougher than some other courses. Be careful in the cave, and you can chain quite a few boosts.
-The left route at the fork in front of the giant Death Adder statue (after the drawbridge) is the shorter route, and contains an extra stunt jump.
-Dropping off the track to the lower route during the big turn before the swinging axes is a good idea - the water route is much shorter than the land route, and the boiling cauldron hazards are easier to dodge than the enormous swinging axes.

-A character with great handling is a must here, and will lead to better overall performance than a character with a high speed stat.
-Drift EVERYWHERE. This track is built for drifting, and there's not much else to do given how tight it is.
-Don't be afraid to slow down a tiny bit on the corners. Slowing down to avoid hitting a wall is better than slamming into it at high speed (so long as you don't slow down too much of course!).

-The car section gets narrower and twistier each lap. Watch out for this!
-At the section where jetski and fighter-jet holograms are passing by overhead, the side of the road you (or more specifically, the person in first) drives on makes a big difference. Driving under the jetski leads to the water section while driving under the fighter leads to the air section. The air section puts the AI at a large disadvantage as they cannot adjust their paths to avoid the electro-shock fields that move in/out across the course.
-There are lots of risk-boost opportunities on the wide-open air section. All of the holograms except for the Space Harrier snake-thing are non-solid, so you can risk-boost off of the circular platforms behind them.

-All four classic courses are highly ideal for drifting since they were initially designed for Sonic & SEGA All-Stars Racing, where drifting was a much bigger part of the game.
-If you're wondering why Sunshine Tour and Roulette Road were deemed cool enough to return ... they both had more features in Sonic & SEGA All-Stars Racing that were for some reason removed for this game, which originally made them stand-out courses. There were springs to keep you off the walls in Roulette Road and moving mylar balloons as hazards on Sunshine Tour, plus a see-through track in the rooms with the giant heads. They were much more fun there. :P