So here's the pitch: I bought a new router, and it had a coupon in it for one if the following (my pick):

• Need for Speed Undercover  (Free)
  
• Need for Speed Carbon (Free)
  
• Need for Speed ProStreet (Free)
  
• Need for Speed Shift (Free)
  
• Need for Speed Hot Pursuit (33% off)

So here's the pitch: I bought a new router, and it had a coupon in it for one if the following (my pick):

• Need for Speed Undercover  (Free)
  
• Need for Speed Carbon (Free)
  
• Need for Speed ProStreet (Free)
  
• Need for Speed Shift (Free)
  
• Need for Speed Hot Pursuit (33% off)

I've heard pretty good things about Shift. Hot Pursuit is the best one but you already know that.

Out of all of the free choices, I think I'd choose Shift. It's kind of a bland sim-style racer compared to some of the newer offerings available in the genre (Forza 3 and GT5), but its in-car view is the best out of any racing game that I can remember. It should be more fun for you than any of the other free titles.
 
Here's one of the better videos I could find on YouTube of the in-car (all of which seem to focus on Nurburgring and nothing else):
  

Carbon.

Wasn't Shift completely awful?

Just to note, Shift is a sim racer a la GT or Forza while the others are arcade style racers. So if you are not a fan of sims then I would steer clear of Shift even though it is arguably the best choice outside of Hot Pursuit.

" @Azteck: I think you're thinking of ProStreet. Shift was the best NFS since Most Wanted, until Hot Pursuit came along. To OP: Get Shift "

If you don't like sim racers choose Carbon.

For humour, over-the-top B-movieness and LOLRIMZONCIVICS, I'd say go with Undercover.  Shift is probably the best of the games on that list, though.

Shift or (maybe) Carbon. But when you have the money, definitely get Hot Pursuit. It's so good.

SIgh...
 
So I got some money at the end of the month, bought Hot Pursuit, and then my power supply fan starts making noises. I'm really unlucky -_-
Now I'll have to fork over triple the cost of this game for a new power supply and assembly! I really wouldn't want the PS to blow and take some other parts with it -_-

I think you should get NFS: Undercover, Shift is more of a serious racer and Carbon got really bad reviews IIRC. It's a shame that Most Wanted wasn't in there, that's a great game.