A lot of these games were good - I think there were only two I hadn't heard of. Another World's sequel, Heart of the Alien, was good. There was a third, too, I believe, but I may just be thinking of Flashback and it's 3d redux. Blackthorne was another of those awkward Prince-of-Persia-esque 2d one-screen-at-a-time things, but pretty easy. Actually, all of these games were easy once you understood the puzzles. Another World takes me about 8 minutes now, I think. Never figured out the tank, just mash buttons and you'll eject eventually.
Metal Storm was always one of my favorites. Never understood the physics behind it, but it sure was sweet. And hard. Had the Gradius respawns.
Jet Set Radio Futures was one of the bigger games for the XBox in the earlier days of the console. Not that it ever recieved much acclaim because its original, Jet Grind Radio, was better on the Dreamcast... and even that wasn't very good. It was packaged with SegaGT, if I remember correctly, just like Tetris Worlds/Star Wars.
Anybody remember Silhouette Mirage on the PS1? Featured a little robot "guardian" who was red on half her body and black on the other. You'd fire Silhouette or Mirage shots depending on which way you were facing, which would either drain health from enemies or damage them depending on their polarity (Silhouette or Mirage). Here you see some of the initial concept for Ikaruga, actually. The gameplay was cool. You couldn't just run-and-gun ala Contra, but rather had to adapt to whatever craziness was thrown at you. In addition you could mug enemies for money, reflect shots of the same polarity as you, and buy weapons from an arms-dealing bunny rabbit with an ice cream cart. My favorite boss was an anime chick's face on a giant flying fish body called a Guardian Angel who attacks you for not buying flowers from her while you're on a Semi truck convoy. It was made by Treasure, who were a good portion of the dev team behind Contra 1,2, and 3 before seperating into their own company; they also made Gunstar Heroes, Alien Soldier (import only Genesis/Megadrive game that's a fantastic arcade-style boss rush), Guardian Heroes and Radiant Silvergun (two of the best-known games on the Saturn), Astro Boy on the GBA, Ikaruga... etc. They have a standard for excellence, even if they do phone it in on occasion (Wario World on Cube).
Another PS1 game: Starfighter Sanvein. I think it was made my X1 Games or something like that. You choose a main and sub weapon for a little starfighter which determines your manueverability, then choose the order of the levels you want. You get 600 game seconds to beat the game, which is increased by killing bosses quickly and lowered by getting hit. The interesting mechanic is that each area is a series of hexagons that you go into, one at a time, to get to the boss. You don't have to hit them all, and can beeline it straight to a boss if you want, but for every hex you've beaten that is touching the area you're in your weapons are powered up 1 level. So there's a happy medium between getting to the bosses as fast as possible and killing some of its surrounding little enemies first.