Growing up as a kid, I had Tony Hawk's Pro Skater 3 for the PS1. It was a pretty fun game, and to be honest now I'm so used to the graphics on that game, that the PS1-style graphics with pixellation and texture-warping just seems like the ideal "look" for the game. Well, we also rented Tony Hawk's Pro Skater 4 for the PS1 too, though I don't remember that one as well. With that, I also have some experiences with other games in the franchise: THPS2 was one of the very first N64 games I got, THUG for the GC was a game I played as my uncle had it, my friend had THPS3 for the GC, I had another friend with American Wasteland for the Xbox, I also had THPS4 for the Xbox and Project 8 for the PSP, etc. I also played Tony Hawk's Pro Skater 2X too, etc.
While there are other extreme sports franchises, the Tony Hawk series is probably my favourite. It just feels and plays really well. To be honest, I actually also feel that the 2-minute goal-based levels of 1-3 are more fun than what would come afterwards too. However, that isn't to say that there aren't any other worthwhile games. I also have Mat Hoffman's Pro BMX 1 + 2, which Activision themselves cashed in on in order to get as many extreme sports as possible They also made Surfing, Wakeboarding and Snowboarding games, though I don't have any of those (and to be honest, they also don't look as enjoyable, but who knows, maybe I'd enjoy them too).
As for non-Activision ones, it can get iffy. I don't have much experience myself outside of it; I have Razor Freestyle Scooter for the PS1, but it's cheesy as hell!! I also played a bit of Shaun White Skateboarding and did enjoy it for what it was, but it wasn't amazing or anything like that. As for the ones that are generally well received, there is Z-Axis' Thrasher Presents Skate & Destroy, Dave Mirra Freestyle BMX 1 & 2 (as well as BMX XXX, but that is pretty controversial in and of itself!) and Aggressive Inline. Some other ones are the Skate series and Grind Session.
Alas, the genre is pretty much dead now. Acclaim and Z-Axis both went under, along with the Tony Hawk series meeting a disastrous end with its stretch of Ride, Shred and THPS5, and EA has put the Skate series in limbo. So, what we have to make do with is the classics. What about you guys? Which ones have you tried and enjoyed/disliked?