In your opinion, what types of game mechanics and or things make games replayable?

Take a look at tetris and space invaders. Both games feature only one level, simple graphics and don't even have a story, yet they are practically infinitely replayable. Because the reason you play them is that you want to reach a high score. In other words - competitiveness. In order to come up with an interesting gameplay try shifting focus from content (art, music, story, level design) to the gameplay. If your gameplay is good, your game will be replayable even if it only has one level, mediocre graphics and no story.

More choices.

More eye candy.

A way to master the game that doesn't require endless amounts of time spent playing it, like if you had a unique idea or strategy. Actually, I'm not sure if that's possible. I was just thinking of the MMORTS I am working on.

I have to completely disagree. Look is certainly a factor. But more choices and mastering a game are diametrically opposed concepts. If you master something then the choices are limited somewhat, and once you know it all, things become familiar and uninteresting. For instance in life it is very difficult to become a master of 2 or 3 professions - there is just so much complexity to every topic.

More choices, so many that you must pick a certain area to concentrate on to achieve success in the game. No clearly definable way to win, let the players decide how to win, as in life - open world, rock bends scissors why? Doesn't matter the players will find a way to make a use out of this. Make your world open and free to interact in (it doesn't even need to be too complex - water + earth = mud (fun), water + cold + door = someone trapped inside their house (fun)), let there be much to learn and many mysterious things/restricted areas/actions - giving a player motivation to try and find a way in or to find out about said item/lore.
Some skills could only be taught by a rare NPC in a difficult to get to location. Make the Lore vague - as in life, we love the Egyptians and Aztecs they achieved much and we don't have their complete history. Were the pyramids really covered in gold? Is El Dorado still hidden somewhere in the jungle? Are Moses' powers to turn a stick into a snake possible?

Don't worry about gimmicks like persistent levels and achievements before you have the gameplay down.

I suggest you look into DotA, a WC3 custom map that is (was?) arguably one of the most popular competitive e-sports around. The game had one terrain, no stat tracking outside 3rd party programs, no achievements, no unlocks, nothing. It was pure gameplay and learning what made people willing to play the same terrain thousands of times will (even if it doesn't directly translate into your game) help you.

The most important aspect is variation. Player vs Player games have innate variation because players are difficult to predict. Of course, you need to allow players to be unpredictable if you want a successful PvP game. For this, you can look at anything from Starcraft to Halo; unpredictability creates variation. Variation creates replayability.

Next comes varying degrees of success. While "You've won!" or "You've lost!" certainly work for some games, I'd argue that such a boolean outcome is dull. Take a look at any fps game; you have the same overarching "You've won!" message at the end, but in addition, you have your kills and your deaths. Your team may have won, but your 3 kills and 28 deaths probably didn't contribute. This is a varying degree of success; you succeeded, but you could have succeeded better. That drive to improve is a very important aspect in creating replayability. High skill ceilings and good competitive aspects both improve (but not create) this.

Lastly, direct variation. DotA consisted of 2 teams of 5. Each player would pick from 60+ heroes. This meant that you rarely would have the same composition of allies, and rarer still would you fight the same enemy. I don't think this needs much expanding.

Of course, this is more aimed at PvP, but the same principles can be applied to PvE centric games. Diablo and Diablo 2 are PvE games that create a lot of variation; random loot drops, random dungeons, random enemy spawns. The less likely that the player will be in the same situation twice, the better.

Well, good storytelling is always a good motivator to replay a game for the experience itself.

Another motivator would be for a challenge if the gameplay is good, since you could play on a higher difficulty.

Something that is incredibly important that seems to have entirely abandoned console gaming is variety. If I play the game a second time will anything be different? Will I be able to customize my character in different ways? Will I experience events in different ways? Will I be able to choose different paths? Will I learn things that I might have missed the first time through?

And then a small aspect that I find to be incredibly overused and rarely well executed is new game plus. The only game I have played where I found the feature to be worthwhile was FFX-2, because the level and stat mechanics actually retained balance despite equipment and abilities carrying over.

To me, the greatest amount of replayability I have ever experienced was the original starcraft. User created maps, user hosted maps... See something new, try it out, see something you enjoyed, play it again (the play would still be different than last time). To me, starcraft2's popularity system killed the infinite replayablity aspect. People now play only the top x popular maps...

Which leads me to why? Users. Allowing users to create content, make decisions, have an impact, etc... Since you mentioned more-so the RPG genre of replayability, choices are probably your best bet. Certain choices might unlock a new playable character to party with, or might affect the storyline a bit and you lose certain party members. Maybe you get different endings depending on choices (for this newgame+ would suffice well, I'm sure the grind from absolute beginning doesn't help). Maybe newgame+ would feature story advancement, or fill in backstories more?

The limit is only how much time you want to spend planning, implementing, coding, etc. You could have a 1000 different storylines/choices/character development, but if it takes 15 years to code all the different variations it probably wouldn't be worth it. We have to draw the line at an acceptable point sometime.