If you like games where you have to have precise controls, why not play some shooters? I already proclaimed my love for Ikaruga and Psyvariar 2 elsewhere so let me recommend some others.
Einhänder (PS1). Dual-weapon customizable system. This game has a great techno soundtrack also, just overall a really stylish game.
Gradius V (PS2). Lots of Option trixies and strats.
Truxton aka Tatsujin (Genesis): More old-school type. Simple but creative levels and bosses.
UN Squadron (SNES): Awesome music, lots of weapons and planes, good difficulty level.
Super R-Type (SNES): Also really good music, really fuc
king hard, and you can do a lot of interesting tricks with your Force pod thingy.
Touhou Project (PC):
http://www.doujinstyle.com/touhou.php "Danmaku" / bullet hell type shooter. If you're really into having precise controls this might be your speed.
Action games:
There are probably enough good/popular ones without getting into the obscure. If you're looking for Jak and Daxter type games, the first thing I would suggest is to go play Psychonauts, that game is nuts. I liked the Sly Cooper games as well. Ico is like an environmental puzzle/adventure game. I think it's amazing. The only "bad" things about it is that it could be considered "slow" because it's a puzzle game and you don't really have to do much actual fighting, but that's kind of what a puzzle game IS so I don't buy that criticism.
You could always go play NES Contra and try to beat it without the code. It's not really THAT hard + it's a nice feather to have in your cap. It's a good project for about a week. Also, Mario Lost Levels (aka SMB2 in Japan) on Super Mario All Stars. And I'm sure you have played the Katamari games by now, but if not then you need to do so before you play any other game I've mentioned. Unless you also haven't played Jet Set Radio, in which case THAT should be your first priority.
QFT, except the PS2 version is buggy and horrible.
That's too bad, I played it on DC and forever thought I had missed out on some bonus stuff or something on the PS2 version. I actually think Grandia Xtreme has a -slightly- better battle system, but everything else about Grandia II is better. Grandia is like the only game where I actually wanted to beat every enemy group in the dungeons, because each different combination of mobs requires a different strategy to deal with effectively, and it was actually fun to practice strats and do some trial-and-error.