oh man, R-TYPE FINAL. I’ve finished getting all 101 ships on the yuropean version, and for the heck of it, started doing the same thing all over again when I got the japanese version … because it has a different ending. I was such a fanboy of that game, yes. And easiest difficulty level in J|NTSC version (BABY iirc) was harder than western/yuropean-BABY mode. Such pussies we’ve been …
anyway, with some Irem love (and that's _needed_ not to die because of loading times and tech prowess!=tech craftsmanship), I'd say Steambot (I have been a bad guy and it was cool to _do_ that, oh yeah…), Zetsumei 1.
other titles mentioned already include Ace Combat 4,5+Zero, Katamari 1 (oh yes). SotC, REZ. GT3 is more arcade/fun-racer than GT4, the latter tried too hard to play grown-up and it just never came together. Still 100% the A-SPEC on both …
titles that are missing so far:
ENTHUSIA Professional Racing, because it dared to do things differently. No credits in the game whatsoever, interesting mix of arcade-tracks + Nürburgring, best curated car-roster for years to come.
Valkyrie Profile 2, because it managed to take a 2D battle system to 3D and yet somehow bridge the gap by being 2.5D. And it was a beautiful tri-Ace swansong to the PS2. Just don’t get the PAL version, I imported the US-version for a good reason …
WRC Rally-games - 4 sticks out because of first-time-I-played-sth-like-that bonus, though I’ve played a lot of Evolved, the last one on the PS2. Newer rally games on the 360 and even Seb Loeb Rally on the PS4 are basically prettier versions of 4, with newer cars, cooler GFX and stuff like headlamps etc., but WRC4 on the PS2 just managed to nail it, just felt right.
other titles were improved upon in later gens, be it lumines, ESPgaluda, Sylpheed, Magna Carta, Star Ocean …