Wow, Warhawk actually looks like a lot of fun. I haven't actually played that one, so that might be what I go for next. See, if you look at the video, that's exactly what I'm talking about, that strange little period between the 16-bit and 32-bit eras... where you have 3D graphics and more complicated controls, but you still get stuff like the cheesy FMV cutscenes that you'd see all over something like the Sega CD or 3D. Even if it only lasted for a year or two, I love that kind of era. Disruptor's great for that kind of thing, too. Actually, I heard once it was going to be a 3DO game, and it definately has that kind of feel to it.
I can confirm Ape Escape's really good, too. It's pretty interesting to have a 3D platformer where the collectibles try to avoid you and actively fight back. The whole dual analog thing works really well, too. On the subject of platformers, I'd recommend anybody who's interested in Crash and Spyro start with the second game in each series. Spyro 2 is a lot less easy and generally less empty feeling in its levels, while Crash 2 is much, much fairer in terms of difficulty.
Great video, though. Definitely shows off the variety on the PS1 and all the genres you could find on it, although there's quite a few games I'd say they missed.