The Metal Slug series
, especially 1-3, has some incredible boss fights. Most of them are pattern-based and very predictable, but oh-so-much-fun! My favorite, or at least the one I remember most, is the climbing thing from Metal Slug 2/X, stage 2 (Egypt).
Apogee's Stargunner is another game with great bosses, one for each stage. (About 30 total, IIRC.)
That's one of the things I miss from the 2D days of yore. Most 3D games just don't have the same sort of ginormous, what-the-fuck-style bosses, nor the immense feeling of catharsis you get from beating them. It was fun to go through each stage knowing that something terrible was lurking at the end, wondering what horrible tricks the designers would unleash upon you this time. Half-Life 1 is the last 3D PC game I remember that did it well. (Half-Life 2 utterly sucked in that regard.)
EDIT: Oh yeah! For more intelligent boss fights, see the 2D Zelda series, especially Link's Awakening and Minish Cap.