Some I haven't seen mentioned.
Red Faction: First one was imperfect, but great nonetheless. The whole geomod thing, though underutilized, was just present enough to raise it beyond the generic shooter it'd have been otherwise; I remember once when I didn't have much health, and just walking into this room meant getting killed every time. I had a bunch of explosives with me, so I blew through the side wall, went around, and ambushed whatever it was that was getting me. Red Faction 2, on the other hand, was kind of a mess. Still played through the whole thing, but it was totally soulless and stripped down. Probably one of the most forgettable games I've ever played.
The Longest Journey: So, Dreamfall isn't necessarily a bad game, but it's still completely devoid of the charm of the original. The first one sucked you in, while the second one relied mostly on familiar locations and characters from the first to carry its mostly-incoherent plot to an even less coherent conclusion. The Longest Journey, on the other hand, is a complete game with a good (some would say great) story, making it the vastly superior game, even if a lot of people have trouble with that rubber duck puzzle.
Actraiser (SNES): This was an awesome mix of god game and platforming. The sequel went, "Hey, remember all that fun god game stuff that you had fun with? Screw that, now we're 100% platformer." It was a much less interesting game for it. I'm not even sure anyone remembers that there was an Actraiser 2.
Pokemon (GB): I remember playing Pokemon Red and thinking that it was actually pretty good. Now there are a million and a half sequels with a billion stupidly-named pokemon that look like mentally-handicapped inbred versions of the first 150. I was really easily entertained as a kid, but even I recognized just how stupid the whole thing got.
Mass Effect: I don't exactly hate the later games in the series, but playing them back-to-back made me see just how much greater the original game was in virtually every aspect. Most notably, the storytelling was tighter and made more sense (2 and 3 seemed designed like the show 24, with certain moments set up purely for random shock and subsequent soap-opera drama), and leveling up actually felt like it had a pretty tangible difference in combat while the later games relied more on player skill.
Soul Calibur (Dreamcast): This is from way back when the characters still dressed semi-modestly and gameplay mechanics were the game's top priority. Now it's all about the jiggly jiggly and making people uncomfortable by putting Ivy in costumes that make
Milla Jovovich's outfit early in The Fifth Element look like winter attire. They also strike me as much less fluid, balanced, and responsive than the original.