I think I tend to agree with you. In many cases, developers see what works and what doesn’t work and try to distill what works and make it better and trim off what doesn’t work. However, there are many cases where sequels get botched, and I’m sure others can point them out more readily than I can.
Civ I was ok, **Civ II **was a masterpiece.
Also-
TimeSplitters 2
Twisted Metal 2
Street Fighter 2
I dunno, I thought it was a logical leap forward (though a huge leap). I was a huge fan of GTAs 1 and 2 precisely for the reasons cited so often for 3 and up as being their groundbreaking feature: the non-linear, do-anything “sandbox” gameplay.
Now, if I’d cited Wolfenstein 3D from Muse Software’s Beyond Castle Wolfenstein… that’d be a bit of a stretch! 
As far as sequels that don’t get better with age, I know fans of Street Fighter, Tomb Raider, Mortal Kombat (just to name a few) felt that those series all suffered eventually when comparing later sequels/spin-offs to earlier works-- Tomb Raider 2 was better than TR3, for example. There’s also a problem with many series when original developers leave, and the company which owns the brand brings in a new developer… I seem to recall the Twisted Metal franchise suffering.
Curse of the Azure Bonds as a sequel to Pool of Radiance stood out for me partially because the next game, Secret of the Silver Blades seemed to forget any lessons they learned about pacing and plot. SSB had long sections of game filled with pointless encounters that just sapped time and your soul. There was a portion I remember where you had to travel through some ravine (down a hallway for all practical purposes) and, every three steps, there was another “random” encounter with frost giants and griffons. Three more steps, another encounter. Then you’d be getting low on spells and health so you needed to camp which led to more random encounters. None of them led anywhere, it was just a massive timesink to get to the other end of the canyon. You couldn’t pay me to play through that mess again wheras I’ve played CAB several times including on DOS emulator.
I never played the sequel to SSB (the Menzoberrean one?) but my understanding is that that one was even worse and went straight to hell.
But they brought back much of the original talent for TM: Black, which was a very well done game.
I vaguely recall that. I ended up getting burned on TM3 (as did many others!), and read bout prmises that Black was back to form, but by the time of its release, my time and money were diverted away from gaming.
Kind of a shame, I will have 7-8 years of gaming to catch up with once I’m finished with school; I imagine I’ll end up not getting to spend much time with worthy games that have come out since the Dreamcast faded…
Since Star Control 2, Orion 2 and Max Payne 2 were mentioned already…
System Shock 2 is a lot smaller, but much more elegant then Shock I. One of my all time favorites. I think I know every item that is to find in this game.
Dune 2 was one of the first realtime strategy games, and set the style for a generation. It had it’s flaws, but was great - though Dune 1 was a completely different game. I still remember the fear of the AI’s Death Hand. :eek:
Monkey Island 2 is still the best of the trilogy. (No, I didn’t like part 4 :P)
Xcom 2 - Terror from the deep has slightly better graphics than the original, but I like it a lot more - the whole setting is cooler. Xcom 3 - Apocalypse is the best one of the franchise, but I think I am the only one who thinks that. Nothing like mowing down Aliens with the Toxigun. 
Diablo was probably the game I logged the most lifetime hours in, until the release of…Diablo 2.
The main Mario series improved with each game for the first 5: SMB1 < Lost Levels < SMB2 < SMB3 < Super Mario World. But Super Mario World is the pinnacle of platforming and has yet to be bested (I’m not sure it ever will, at this point).
Master of Orion was a great, if unbalanced, 4X game. Master of Orion 2 is still regarded as the best sci-fi 4X ever made.
EDIT : in the same vein : Heroes of Might & Magic was good. HoMM 2 was great. HoMM 3 was awesomtastic. Then it finally started going downhill. Number 4 is a rotten piece of crap, 5 is… meh-ish. Good, but no Heroes 3.
On the other hand there’s plenty of sequels where they fail to learn the lessons of the original in order to refine it and instead pile on bloat. “More weapons! A few more smaller levels! New concept placed in bullet points that is only used at a few carefully selected points!” The Tomb Raider series could be a study in that.
Pool of Darkness. It does feature Drow on the cover but Menzoberranzan was a different game.
It was about a pool… of darkness… and…
I seem to have completely repressed this one. And I still remember things about Dark Queen of Krynn and we all know what a crapper that one was.
Oh, of course. You can find a worm in the apple of sequels and I don’t think anyone is really saying otherwise. When done properly, and if warranted, sequels should almost certainly be better.
Also, I liked Pool of Radiance: Ruins of Myth Drannor, but not as much as the original on the Nintendo. I lost track after that. What Pool of Radiance game is most recent?
I think Majora’s Mask was better than (gasp) Ocarina of Time. Anju/Keifei sidequest notwithstanding.
Actually, probably the only bad direct sequel in the Zelda line-up is 2, and it’s still a pretty damn good game since it’s only bad by Zelda standards (with Phantom Hourglass getting an honorable mention JUST for the tower).
I didn’t play Majora’s Mask, but Zelda 2 was a helluva game. Unfortunately, it gets looked at like Super Mario Brothers 2, where it did something a little different, it was initially loved, then despised, then very quickly loved again after people (for lack of a better term) “got it”.
Amusing how both of those -also- serve as great examples of games that had terrible sequels. 
Also, I may be strange, but I didn’t really feel MOO2 was a huge leap from the original. It was shinier and more customizable, but at least as unbalanced, added a ton of unpleasant (for me) micromanagement, and essentially just became Civ…In…Space -ace…ace…ace…
Made me kinda sad once the shiny wore off.
Blasphemy! While I’m not one of those people who think Ocarina of Time is the greatest game ever (it has massive pacing problems for one), there’s no way Majora’s Mask is the better game. It’s just… not.
But a few that are better…
Contra III is light years better than Super C and better than Contra only because of technology’s advance. Contra: Shattered Soldier and Contra 4 were both amazing games, but I’m not sure they’re better than III.
Speaking of SNES launch games, Super Mario World is the best Mario. Anyone who says otherwise is just a liar.
Oh, I’m also one of those people who think Ninja Gaiden III is the best NES one. Go ahead and look down your noses at me. It wouldn’t be the first time.
And a sequel where they blew it…
Total Carnage is a pale, pale imitation of Smash TV.
One of the problems with living in England is that the video games I knew as a kid aren’t the videogames you knew as a kid. For example, the Contra series was called Probotector in the UK, and the numbers are all different. I think Contra III was Super Probotector, but I’m not really sure.
I think Total Carnage was Super Smash TV, but I’m not sure about that either.
Prince of Persia: The Two Thrones is a damn good sequel and conclusion to the Sands of Time Trilogy. It stands out even more because Prince of Persia: Warrior Within is a pretty awful sequel, so bland and generic in everything but the platforming that it doesn’t really deserve to be called a Prince a Persia game.
I wouldn’t burn you on the Ninja Gaiden one. 3 was better than 2, for it improved upon the previous. Freak.
This was first thing that popped into my head when I read the OP.
The original Street Fighter was damn near unplayable, and I’m not sure it would’ve been even if those pressure sensitive buttons hadn’t always been broken.
Street Fighter 2 is a classic that revolutionized arcade fighting games in the early 90’s. I know AOF and KOF/FF came out around the same time but I’m fairly sure SF2 was first.