There seems to be an unusually high number of people talking about racing games on these forums recently. Good!
I've spent literally thousands of hours playing the Forza franchise. I love it so much. I've never come across a racing game which just feels so good to drive in. The handling model is exquisite. I can't say which one I like the best. I can't really pick a single one that I've preferred or thought was better. To me it's just one huge evolving experience over time since I play them pretty much constantly. It's not like I play the game for a few months and then start over when the new one comes out, it's like the next game in the series is a whole new build of the same game. Like a 2.0 (or 3 or 4.0) version of the game.
I used to like the NFS series, but they went downhill. Underground 2 is one of my favourite games of all time but after Carbon they pretty much all turned to shit. It's been painful to see how far this franchise has fallen. It wasn't just suddenly crap one day, it was a gradual decline. If seeing the change between Fable 1 and 2 was like seeing a friend falling off a cliff, watching NFS was like seeing them die of cancer.
I also love the Burnout series. I loved it right from the first one, which I had on Gamecube. Because of that I never got Burnout 3. I was waiting for it to come to GC but it never did, so I just skipped that one and got Revenge on PS2 once I got one. I've also spent a load of time on Paradise. That game is great, despite what some people say about it. It sucks we haven't got a real new Burnout game since then, though. And now Criterion are focusing on NFS, so it doesn't seem likely we'll get one in a while. At least they might be able to bring NFS back from the grave, although I was not enthused by their previous attempt to do so. MW looks better despite its stupid name.
I really love the TDU games as well. I had more fun with the first, but I can't deny that the second is technically better in many ways. But no other racing game is quite like either of those. They are just so massive. There's no better road trip/Gumball simulator than those games, and playing it with friends is a blast.
I love Race Driver GRID too. I've always had a soft spot for Codemasters, but the DiRT games never really got me interested. I'm sure they're great, and I've considered buying them on many occasions, but I just simply prefer tarmac racing over dirt racing. I loved GRID's realistic tracks and cars mixed with the really intense driving feel. The myriad of different event types was another great thing about the game, and the presentation of everything was top notch, just like pretty much all the other recent Codemasters racing games. I can't wait for the sequel.
Flatout: Ultimate Carnage is another great one. I like this one because it's a real sleeper hit. It's a really fun demo derby type game with lots of cool special event types that usually involve throwing your driver out of your car using him to score points in varying games, like bowling, baseball, basketball, etc. The races themselves are genuinely fun too. They're chaotic, but they do take skill. The cars feel appropriately wobbly, but not annoyingly so. They're still predictable, most of the time. I advise people to check it out. Ironically, the best way to make money on the game, though, is to lose the race on purpose. Going backwards and just wrecking people as hard as you can often gets you more cash because of bonus score than you get for actually winning the race. The game also has a really great soundtrack. Lots of little known but really good rock bands that fit the tone of the game perfectly.
