Are there any games that play entirely differently depending on characters, spells, weapon loadouts? Are there any games that feature randomized enemies or environmental hazards that differ each time you play? Are there games where New Game + mode adds NEW events, enemies or obstacles NOT found in the first play-thru? Usually New Game + means just a higher difficulty level, but are there games where they REALLY mix it up?
Loot games usually give you a TON of options and replayability too...
I --LOVE-- the random element of Rogue-likes because you never know what to expect with THEM...
...but what ELSE? Are there action games, FPS... anything else that has GREAT replayability that I'm just missing here?
Oh hell this has been around for ages.
Just look at Castlevania III: Dracula's Curse.
When you took Grant or Alucard as a partner, new paths opened up to you. More importantly though, the boss battles could have a completely different feel depending on who you took. Fighting with Sypha for instance completely changed up how battles would, depending on what magic spells she had at her disposal.
Looking down the 16-bit era you've got a game like Seiken Densetsu 3.
6 available characters, but you could only select 3. And really, the main story was fairly unique depending on which of the 6 you picked as your lead character. Outside of the story, the battles could be very different experiences depending on who was in your party. If you had Carlie you had a dedicated healer who couldn''t fight for crap, but she could keep the team going until they got the job done. Angela, the sorceress, could nuke the shit out of any monster, and could end battles extemely quickly assuming she didn't die in the process. And if you picked a team with all fighters, you'd breeze through almost every regular battle, but you'd have to find very specific strategies to deal with bosses. And each of the 6 characters would undergo class changes, and that added an extra dimension to the game. In the end game Duran could fight as a Paladin and could heal as well as fight. But he could also end up as a Duelest, and be a pure killing machinem but couldn't support the team with any magic. So, yeah there was tons of replayability in this 16-bit title.
What you're missing big on are games focused on mastery. You can find this in sports and strategy games, and pretty much anything competitive online. Particularly this is the case when games are contained in rounds, like a deathmatch an FPS or a full 9 innings of baseball. You play through, someone wins, someone loses, then you do it all over again, looking to improve on your mistakes and get just that much better. It's the driving motivation for most of what we do. It's how we have so many musicians and artists and endless other talents. Some just apply them to, say, plow through every Resident Evil or be the last remaining person on earth playing Killzone 2.
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Tell me to get back to rewriting this site so it's not horrible on mobileThere's a **not so** obvious answer also staring me in the face right now:
One on One Fighters --SHOULD-- be ridiculously replayable --BUT-- the online community comes and goes fairly quickly --AND-- I don't know if this is true for everyone or not: I rarely take the time to learn each and every fighter in a fighting game. Instead, I find the one or two that suit my play-style and stick with 'em. I wonder how long one would last if I tried to master each and EVERY character?
Games that require mastery? Allow me to present Heroes of Might and Magic 3.
The absolute most amazing turn based strategy game ever created. Any schlub can get through the missions on standard mode, but try playing on the harder difficulties. The game because something akin to three dimensional chess. Do you try to expand you territory quickly and get resources? Or do you try to concentrate on building an army? Do you go after your enemy as quickly as possible or do you delay confrontation in hopes you can grow stronger than he can over time? And once you do confont, how do you handle the battle? Do you take it to him quickly or allow him to come to you? Despite being 15 years old it's one of the most brilliant games ever made. I still play it every few years, and get sucked into like very few games can do.
I was typing mine while you were typing yours, Yoda, but yeah competition adds alot to replay...
I've been thinking about this topic for a while, before Aspro asked the "Game you would play for the rest of your Life" question. It would take a VERY replayable game for me to answer that. I simply CAN'T play the same sequences again and again NO MATTER how good the game was. I need some kind of variance and not something that relies on other people to make it work.
I am going to put an answer in that topic now, now that I've had time to consider, but I'd like to explore this topic more!
Sandbox games (Simcity and The Sims) where there are no set goals and no way to "win" the game, are the most replayable and enjoyable for me. Want to build a futuristic city in the shape of a Goomba? Do it. Want to play an astronaut that has a giant swimming pool in his/her living room, and also sells toilets out of his/her basement? You can do that too. Enable cheats and go hog wild building anything you want with unlimited money, or start a game with one Sim that has zero money, and have them work their way up from being a homeless person to a millionaire with 15 kids. Tell any story you wish. I saw a Let's Play where a guy created a bug-eyed psychopath that made his money by hacking computers, and went around town luring unsuspecting A.I. Sims to his home dungeon. It was sick, but funny.
I feel like modern games these days are designed to be more replayable than games in the PS1 era were, but I rarely replay anything myself just because there's too much to choose from and too little time. Unless of course I go insane and replay an entire franchise like I'm doing with Resident Evil right now. 
In fact maybe its just my age and the way I look back at certain times so fondly, but I still replay the old classics more than I replay anything more modern despite the fact that these modern games, as I said, have more replayability built into them. Its nostalgia.
If I was still 18 years old I can imagine playing through games like Bloodborne or Skyrim an endless amount of times. I still come across the odd game these days that I will do that with, like the Mass Effect games. But for the most part, I'm more apt to replay the old shit instead.
Dark Souls 2 got me thinking: Between the different weapons, spells and character builds, you could play the game over and over and play it quite differently each time. I've never beaten a modern From game yet; maybe Bloodborne will be my first. I don't know how much New Game + differs from the original play-thru in anything else but difficulty, but playing it again with a strong but slower weapon is something I hope to do...
The concept of Action Adventure Role Playing with different classes is nothing new...
...but it's usually those types of games that are very replayable.
Sometimes there's different character classes and HUMONGOUS worlds, but I wonder if there's more games I've just not looked into yet... besides this genre...