Seconding Burnout 2, Kinetica and NFS Hot Pursuit 2. NFS Underground 2 is also very good.
I'm also going to throw in a recommendation for the Choro Q games (Gadget Racers, Road Trip, ChoroQ), which are racing / RPG hybrids that are very different from pretty much all other racing games.
Jak X looks really cool, but I've heard it corrupts memory cards???
On slims, the autosave is bugged and will corrupt cards. You can get around this by never allowing the game to autosave, ie, put the card in when the game starts up so it loads, then taking it out after it finishes loading. Then don't put the card back in until you're at the menu and save manually.
It's worth noting that the PS2 version of Wipeout Pulse also corrupts cards, and unlike Jak X here there's nothing you can do about it, as the problem is not directly related to saving, it can occur after any race and saving any time after the bug occurs results in a corrupted file. The only way to play through this game is to keep your save backed up to a separate card at all times and re-format the card every time it corrupts.
http://terosclassicgaming.blogspot.com/ - Watch me beat "SNES Biker Mice From Mars" http://www.backloggery.com/tero - My backloggery
I played all those games you listed except Excitebots.
You NEED to get Burnout 3 Takedown. I also recommend the 2nd, Burnout 2 Point of Impact.
Burnout 2 is the best arcade racer I played where you have to dodge oncoming traffic. The traffic dodging in burnout 2 was excellent. It would be my favorite arcade racer if it wasn't for Burnout 3. Basically, B3 added to the series the only thing that was not in B2 that would make the game crazier and even better, that is being able to make your rivals crash. In B2 if you hit a car you crash and it could also happen to the rivals, but hitting them yourself would not make them crash. In B3 hitting the rivals to make them crash is one of the biggest aspects of the gameplay. B3 also has more cars to pick from and better graphics than B2. However, from an arcade racer point of view, both, B2 and B3, are excellent. I liked those 2 more than all the games you mentioned. SSX3 is good too, but the burnout games are better if you ask me. Also, I tried Burnout Revenge as well (rented it for a weekend) and my opinion was that I still liked Burnout 3 more. Revenge added a few new things to B3's elements, but overall it did not feel better than B3 and I liked B3's feel more (some elements of Revenge, such as running through oncoming traffic instead of dodging it, did not feel better). In you case you wonder why one might want B2 when there is the better B3, there is one aspect of B2 thtat was better: the traffic dodging. B2 had much more of that than B3. In B3, much more punch was given to "taking down" rivals than to dodging traffic. If you can only get one though, the definite choice is Burnout 3.
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