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I'm not sure who started it, but over the past few couple years, most shooters have been adding in a survival mode, and player response tends to be extremely positive. In my own case, I'm a huge fan of Gears of War 2, but I've never touched the campaign: I just play Horde mode.
If you analyze these against prevailing viewpoints on what makes a game good, you would expect them to be generally uninteresting: No story, no character development, no puzzles, unchanging landscape, etc. So how is it that you can cut most of a game out and find something that many people like even better than what you originally created?
First, survival mode is pure core gameplay. All of the things I listed above can be fun, but they can also be a distraction from the fun (if the core game is good enough). If you want to sit down and shoot some stuff, you don't have to wait for cutscenes or play "Simon Says". Further, instead of trying to learn new landscape, you're focusing on developing tactics for an environment that you're already familiar with. Basically, survival mode just focuses on the best part of the game and tosses out the rest.
Second, survival mode is less scripted. Many of us don't feel much satisfaction from following the pre-planned track that the designers came up with. In campaigns, vehicles, weapons, cover placement, and many other things are carefully placed so that each player runs through roughly the same experience. In survival mode, sure there's careful placement, but there isn't a clear path or an apparent "best" method. It falls on the player's shoulders to find the method that works best for him in a given situation.
Finally, survival mode has unlimited (or at least absurdly high) difficulty potential. Shooters tend to do a better job of implementing high difficulties than most games do (though you always have that crowd who wants something harder), but even in those, the situation is often so scripted that there's not much room to formulate new strategies (i.e. if you can't get headshots off faster, this part will always be impossible on top difficulty).
With that in mind, there's no reason that similar gameplay modes couldn't be made for different genres. Viewtiful Joe could have had an amazingly cool survival mode for a minuscule amount of development time. Zelda could have a carefully crafted room that allowed you to make tactical use of all of your gadgets to hold off waves of enemies.
Finally, this would be an awesome feature to add to RPGs, particularly those with a higher tactical potential. In games like Baldur's Gate, Final Fantasy, or Fire Emblem, I'm constantly working to develop the perfect, super-powered group, but the only thing I can do with it is play out the script (with the occasional side-quest thrown in). In fact, if I'm successful in making my super-party, the game becomes really easy.
When you've finished carrying your party through a 40+ hour scenario, it would be cool to have a gameplay mode simply designed to test how awesome you managed to make them. Heck, I'd probably replay some RPG's in their entirety with my entire focus devoted to making a group that could get as far in this special mode as possible.
Overall, I believe that in nearly all games with fun core gameplay, there can be a lot of added value for little cost by adding in a pure gameplay mode. I just hope that more designers start to see the potential.