Update:
Since posting my below review it should be noted:

• None of the below mentioned issues have been fixed, or even remotely addressed. The developers are fundamentally and completely deaf to any and all community feedback and/or taking basic quality assurance measures in maintaining the game.
  
• Multiple new, game breaking issues have been introduced, and game balance continues to deteriorate. Additional pay to win premium vehicles have been introduced, as well as extremely unfair ingame events based around squeezing money out of players through the game's online marketplace,
  
• The game continues to be based around a single core design concept: strongarm players into paying exorbitant amounts of money through intentionally damaging the quality of the core gameplay loop and dangling solutions in front of the player that must be repeatedly paid for.

The game is, has been, and will remain utterly terrible.

Original review:

As a disclaimer, I exclusively play this game for the ground forces mode, so won't be addressing the air combat or naval modes, though in general many of my larger points carry over in some way.

First off, what this game does well:

• The modeling of the vehicles is amazing. Both in terms of detail and (mostly) in terms of handling, the models and effects for each vehicle make for a truly beautiful experience, especially when compared with other competitors in the armored combat game genre.
  
• The actual basic gameplay mechanics of the ground combat are excellent. The realistic way in which vehicle damage and dynamics are modeled gives the game a weighty feel that captures the subject matter with enjoyable heft. Driving a tank in War Thunder feels much more fundamentally appealing than in other competing games such as World of Tanks.
  The rush of successfully scoring a kill in armored combat is awesome, and has kept me coming back for more despite the game's many glaring flaws.

With that out of the way, here are some of the reasons I do not recommend anyone pick up this game, even at the entry price of free:

• The ingame economy and progression system is an exploitative, broken, and endlessly aggravating mess that has been terrible since the game first launched and has received only the tiniest of improvements over the many years it has been in active development. The rate of gain for 'Research Points', the experience points used to unlock new vehicles, and 'Silver Lions', the currency actually used to buy things, are both horrifically low, with the express goal of getting you to purchase 'Golden Eagles', the game's shiny play money that costs real money and can be used to effortlessly breeze your way forward so long as you're willing to drop hundreds if not thousands of dollars (US, or your regional conversion) into the game.
  Rewards for gameplay are terribly low in the first place, but only get worse when you realize that the game makes you pay to repair your vehicles and buy more ammunition after each battle. That's right, if your vehicle is damaged or destroyed in a match, you have to pay Silver Lions to repair it. Even worse, each vehicle has unlockable ammo types, which are almost always much better than the vehicle's free stock ammunition, each round of which will cost you more Silver Lions to purchase. This gets especially bad with high tier vehicles, the constant hype machines that the game uses to lure people in, resulting in many matches where you will lose significant sums of money if you miss a shot or have your vehicle damaged or destroyed. Given that the whole point of the game is to fight other players using, you know, tanks with guns on them, you will generally end close to 50% of your games looking at being charged for your insolence in thinking you can actually play the vehicles you spent hundreds of hours grinding to use.
  And the vehicle grind? If you want to have the privilege of driving that shiny M1A1 or T-80u you had better be prepared to play every day for several years to top even one nation's tech tree, which will probably be soured in the end because of the game constantly introducing unbalanced new units instead of fixing any of the glaring issues with the economy and progression system.
  
• The balance. There is no balance. Vehicles are thrown with minimal concern across the Battle Rating (a number used to quantify a vehicle's power and match it with similar vehicles) field, constantly leaving you fighting much more powerful units as you painfully claw your way up the tech tree, only to finally reach top tier and...
  There is also zero balance at top tier. New units are introduced constantly to keep the game rolling on announcement hype, with little concern for their performance or the meta they will create. The only pitiful excuse for balance the developers do implement is in increasing the costs for repairs and ammunition for over-performing vehicles, which does nothing but ensure that players who pay real money for in-game currency (did I mention you can just straight up buy Silver Lions with Golden Eagles? No? Yeah.) have a quantitative advantage in being able to operate overpowered units in every match, while those who refuse to invest their life savings into the game are left out in the cold, unable to pay the repair costs on vehicles they spent hundreds of hours earning.
  It gets even better when you introduce aircraft into the mix, because all modes for ground vehicles are actually "Mixed Battles", which let aircraft and helicopters join in on the fun. What I mean by 'join in on the fun' is that in most matches where you play a tank you will end up being killed by a plane dropping a bomb on you rather than being destroyed by another tank. This only gets worse in top tier matches, where helicopters can hover at extreme range from the battlefield and one-shot-kill tanks using anti-tank guided missiles, which they get a large number of, meaning that you have to spend half your time trying to enjoy playing a ground vehicle constantly looking out for and dodging air vehicles. The developers' fix for this? Introduce overpowered anti-aircraft ground units, which are of course top-tier vehicles that you are required to grind for.
  This is all made much, much worse by the design of the maps that you do your actual fighting on, most of which look very nice, but are some of the worst I have ever seen in terms of game design. Sight lines are nonsensical and cover is scattered around seemingly at random, with many maps allowing enemy vehicles to find ways to shoot into one team's spawn locations from the mid point of the map, leaving players respawning late in the game to be instantly annihilated. And added bonus is that there's also nothing to prevent aircraft from camping players leaving their spawns, meaning that you might not even get the chance to see your enemy before a bomb or missile exterminates you 10 meters from your spawn point.
  
• The bugs. There have been reasonable improvements in the game over time in the bug department, but there still remain many annoying issues that will swoop in to disrupt your experience. The game's physics engine is a common culprit, ensuring your tank is launched into the air by a rock or killed by an enemy shell that ricochets through the Nth dimension to somehow wipe out your vehicle. It's less of a pain point than the above points, but it does happen, and it will ruin your day.

All in all War Thunder offers a unique and compelling gameplay experience that I do not recommend anyone check out, because it serves only as a lure for a terribly unfair monetization scheme backed up by countless glaring issues in basic game design that will leave you gnashing your teeth and swearing profusely far more often than delivering the tantalizing enjoyment that the game might otherwise deliver.

It's not worth your time, and it's definitely not worth your money.