A RP that doesn't necessarily need to be based on an already existing property, but uses a unique mechanic for game play, though not alienating for newer players.
Example: a mana system the restricts attacks per post, or something like that.
Maybe a RP that doesn't follow a story necessarily, but follows a series of scenarios that exist in the same event.
Example: a RP that follows the events through a war, but jumps from battle to battle, as a scenario. These battles could be mapped and possible show a "real time" effect on a map (though the affecting the map might be a bit much), however I feel the hard work would be worth it.
Other than that, I kinda just want a RP that puts me in a familiar place, but makes it fresh. It doesn't necessarily need to be "new" or "unique", as long as it is structured well and well written. I personally tend to play more sandbox-type RPs, because I find it easier to incorporate a story, but there has been a few, like Chrome's RPs where the story itself is just awesome, and even if you don't always stick around or are active, it is generally a good read.