I think it depends on the type of game for me. For single player? Replay value isn't as important to me. If it's a good game and I enjoy it I'll go back to it for the sheer factor of playing it over again. I agree with link470 in that having those extras really does make the game shine but at the same time if it's good enough on its own I'll keep on playing it just for the sake of having that good time again, though I may not go back to for a little while. Optional modes definitely help though, like increased difficulty or special stages for post game content.
Multiplayer though? That's where it replay value really shines. It all depends on the type of game but for me, multiplayer should have something that keeps you coming back. It should have optional modes that spice up the game and / or a good amount of content that allows gamers to be unable to see everything in an average sitting. If a game is fun for a little bit but gets repetitive and boring after playing it a few times then that's when it really falls apart.
A perfect example is You Don't Know Jack. Those games are great fun especially with people who haven't played it but the lack of options as far as the game type really bogs it down. It's also easy to get into the habit of memorizing some of the answers, which is mitigated by the expansion packs but ultimately just inflates it instead of adding more to the content. Don't get me wrong, it's a fun game and I'm not knocking it, but I probably won't go back to it unless I play it with different people and even then the experience isn't nearly the same.
Ray wrote:I started thinking about this after Afro's comments on Triforce Heroes.
Replay value wise I'd say Triforce Heroes is kind of average. If you're a completionist, getting all of the challenges gets you the materials for some of the best costumes which is pretty sweet. But if you're not? Most wouldn't touch it ever again. It's a fun little game but there really isn't much motivation for getting 100%. Hell, the reward for beating all challenges is 300 rupees. No seriously. Like, what the hell. You guys couldn't have come up with one more badass costume? I'm fucking rich and own all the costumes at this point, why would I need money? An extremely missed opportunity to add some super costume to the game to motivate those to get 100%. Kind of disappointed honestly.
But this kind of highlights what I believe in replay value: there should be a reason to keep going. Achievements definitely help; while they don't really give anything tangible, just seeing that optional challenge on your wall is pretty awesome. Special modes or gear are a good way to add motivation as well. New Game + is a common example of something that can really spice the game up, especially if you enjoyed the base game.
In the end though, it really depends on the overall length of the game. If it's a lengthy single player game, no replay value is really necessary for me but it is nice to see. If it's a bit short, it would be nice to see something that encourages replays unless the price is low in which case I'm totally cool with that. But when it comes to multiplayer, I'll play a game a thousand times if it's a good time for all regardless of price. I feel those should really focus on creating something that people can keep coming back to and create more memories as they continue playing.