Dirt 2 might end up in an unplayable state once GFWL gets removed. Codemaster has stated that they don't intend to remove GFWL from it, and has instead removed the game from Steam.
Personally, I really liked Race 07. It's a serious simulation-style racing game, so it's not one of those that you just jump into and play, you need to learn how it works.
GTR evolution is an expansion for Race 07. One annoying thing about that game & steam is that each expansion becomes a separate entry, which you need to install on its own, but which are still dependent on the main game being installed.

they are all pretty senseless and probably unfinishable as in you get bored and hit a brickwall of difficulty but these are the games i would consider playing

burnout paradise , the pc version is awful but its still a awesome game it should alone take a while to finish it

need for speed , play the ones that have a story [nfs ug, most wanted 2005,carbon] or focused on racing [most wanted 2012, hot pursuit 2010 ]

Dirt 3 , a good fun game but i recall dlc runing the game a bit in the later parts

f1 race stars another fun codemasters game but the ai is ruthless expect to be enclosed in a bubble and be destroyed
many times

rest all are good but probably will last only a couple of races before you remove them

I would suggest:
FlatOut Ultimate Carnage - a really fun game. Very arcade-y. As a bonus, if you play this you can effectively scratch FlatOut 2 out too because UC is basically FlatOut 2 v.1.5.

Death Rally - the original is better than the remake: I don't know which one you have but they're both pretty short anyway. Shouldn't take more than an afternoon to finish them. The one thing I didn't like about the remake though, was that the races are really, really short: I don't think a single one lasts more than one minute, max. But anyway, like I said: short games, easy to remove them from your backlog.

Don't bother:
FlatOut 3 - haven't played this myself, but I hear everything about it is crap. It wasn't made by Bugbear, so don't judge the previous games based on this.

Oddly enough two of my favorites have been Ridge Racer Unbounded and the cheesey Russian "Death Race."

Death Race mostly because, other than the more recent 'Gas Guzzlers' it's the only other *racing* car combat game I've played where I come in contact with the AI - other titles like P.A.M. the cars have been too far behind me to actually *combat*.

Unbounded...I think I've put in a good twenty hours by now and have made very little progress - The controls are extremely difficult to get used too.

1. There is no tutorial and very vague instructions
2. Each car handles differently - Some don't even use the "Drfit" button (you have to either let off gas or slightly break unless you want to spin out all over the place)
3. Each of the tracks are tweaked exclusive to one specific car resulting in many trial & error attempts until you find the car the developers intended you to use.
4. You won't have the proper car for some early tracks until far into the game

All this adds up to a really difficult to play game but it's still got the best environments & music. The opening city really looks like some place where I'd love to live.

Ironically going back to Ultimate Carnage after failing Unbounded so many times - UC has become terribly easy for me. Having said all of however I'm not certain I'll ever be able to complete Ride Racer....too little progress for the time invested.

Most Wanted feels exactly like Burnout Paradise but with much much less to do.

The racers I tend to hate most are those which were play tested for multiplayer so AI is a tacked on after thought. This winds with titles like PAM, Carnage Racing and Ignite where your competitors are always four minutes behind you and you can complete each race with a first cup gold even with your eyes shut.