Formula 1 2012 is on sale for 50% off today on Steam. Also Dirt 2, Dirt 3, and Shift 2. Those are the best serious racing games on PC.
I find the Dirt series the most fun personally, but that is partly because of my taste in racing. They are all top notch games.
If you are willing to spend $100-$200 on a wheel, the Logitech wheels are the best in that price range. If you go up over the 400 dollar mark, Thrustmaster has a nice wheel set, but everything from their lineup below that price point is substandard compared to Logitech's offerings.
Not sure if you're looking to spend or not but the first game that comes to mind when I think of PC Racing is Trackmania. I haven't played it in awhile and I don't even know if it's still around and still supported but the graphics are decent, it's really customizable and is completely physics-based which I find quite enjoyable. They used to have a free and pay version, obviously you get more with the pay version.
for real racing then shift 2 with the real tires mod is as good as it gets.
the gfx and sim physics are also better than gt5 on the ps3.
for fun then dirt 3 and showdown are pretty decent. if you want an arcade racer then need for speed most wanted 2 is pretty decent. just dont buy NFS the run its crap.