I'm 21 and from the UK, I love all games and own most consoles that came from the SNES era and forward apart from a few I am still wanting to collect.
My favourite game series are the Final Fantasy's closely followed by Metal Gear.
My owned consoles:-
Nnintendo DS Lite
Pc (It isn't technically a console, but I game on it)
A moment can do many a thing for a person, invoke in them countless different emotions, last for what can seem like hours even when only a few seconds in reality. But in a game a moment can make all the difference from a categorized genre that falls neatly in with the rest to the monumental accomplishment that becomes the new bench mark for comparison.
Now with all this vague description aside what I mean in gaming terms is that simply; if you play a kind of game for a kind of feeling the games that give you this feeling are the ones you will want to re-visit, it's common sense. But with a lot of games it's not quite as simple as that because when a moment that is just perfect for someone occurs they will forget about so many other problems or dislikes the game entailed.
In my personal experience I find games with a great story are the best for the moments that pull back to live through the game once again but it doesn't have to be a story based event taking place, sure theres always going to be more drama when a deep story envelops you but if the moment your looking for in a game is much simpler than these sequences can be holding you away from your goal.
Some love the epic fights with huge monstrosities that give them that feeling of accomplishment after having to put all their concentration and skills to the test while others rack their brains on that seemingly impossible puzzle that once complete gives them satisfaction beyond that of which their daily tasks can bring them. Moments in games vary as much as games and gamers do, but if I had to say what I thought was a moment that brought someone back to a game it would be a moment in which the gamer feels a connection to the game.
Going back to some of these bosses still makes me tingle with excitement.
Since games like Half Life 2 and Bioshock showed gamers a new depth of being immersed in a game people believe you have to think like you are the character you play as to be immersed. But to me you simply have to forgot about anything else that is going on and just think about the fun your having with a game. Whether it be a death scene in a final fantasy, to the escape from an exploding planet if the player feels so dedicated to the game that they must concentrate and sit on the edge of their seats to give it their all I feel they are immersed far more than been able to see a world as a character would.
The nuke on COD4 was a great scene to be part of, especially during the aftermath.
Now I know this is a pretty vague description of what I think gives the best replayability for a game but I hope that in reading this you will think of the moments in gaming that always do make you want to go back to your favorite classics. For some it can be the thrill of pushing their skills to the limit and being rewarded with a completion, for others it's the feeling of embarking on an adventure they are deciding. It doesn't have to be a story they follow, but as with the best of stories, if told right they are likely to make the gamer feel more connected and want to go back for this feeling than any other media since you yourself are taking part in it.
Before I go, here are a few more pictures from some of my best gaming moments that I love to go back to: