Shift - Delisted
Shift 2 - Delisted
The Run - Delisted
NFS Heat - brand new idk what you mean there.
Most Wanted - Likely
Rivals - Likely
NFS - Likely
Hot Pursuit is not because they did a remaster and had to re-license the cars.
Unfortunately I haven't found a definitive list.
EDIT:
Remember that this may have been the cheapest, but the entire franchise was on sale as well.
Sorry Shift and Shift II can still be seen, just not purchased.
I'm not sure someone enjoyed original one, but how about:
Need for Speed II
Hot Pursuit
High Stakes
Porsche Unleashed (2 different games)
Hot Pursuit 2 (2 different games)
Underground
Underground 2
Most Wanted (from ps2 era)
UPD: Oh, and I never played this one (DS version is not counting, everything is very bad with it). Need to check!
I own NFS High Stakes, I used to play it a long time ago (Win XP) I liked playing it online (when I was able to find other online players) I'm not sure, but I think it had the same issue that Quake 3 had (it kept asking for the cdkey

) I played it with keyboard, not sure if I ever got my old sidewinder gamepad working with it, it was fun but with keyboard controls it was a little annoying to turn the car (tap tap tap)
I played another one, I think it was NFS Underground 2. There must've been another one that I played, it had Disturbed as one of the Music Artists featured in the game (I think the song was "Down With The Sickness") I'd appreciate it if anybody knew which Racing Game that was and could tell me.
not every GB game was in chibi-style (MK for example or the Street Fighter), but SNK's fightings all were superdeformed and has that "Nettou" prefix when they were released in Japan.
ねっとう

Hiragana (Nettou)
熱闘 
Kanji (Nettou)
a heated battle (Papago)
fierce fight (Google Translate)
You can see the Kanji written on the girl (Left)
They decided on "Deadheat Fighters" for the translation that would make the most marketing sense.
ちび (Chibi) This means "Little" (Google Translate) they use this word to mean the mini version of an anime character (this explanation is for WhatNitrous, I know Dante already knew this one

)
