To explore certain character archetypes in different settings, to see how they change depending on settings and what they experience. I can take Miz as an example. She's been the main character in many RPGs, but given the limitations of pre-written scripts that only goes so far. As an MMO character though, she's turned into quite a few diverse characters over the years.
They all start out pretty similar. Traumatic events, unpleasant beginnings and attaining both a cause to fight for and an "arch" enemy to fight against be it a singular individual, a particular group/faction or even a particular philosophy etc. Since it's roleplaying, I tend to allow them to be somewhat indulging in power fantasy levels of capability since that allows me to explore what they do with the power to affect change. For better or worse.
In World of Warcraft, that meant she lost her life, family, eyesight etc to the Scourge and rose as a Forsaken after Sylvanas freed her mind. The living having turned on her, and everything but Sylvanas wanting her dead... well, more dead... she fully invested herself in the Forsaken's cause and focused on the Scourge/Arthas as the primary antagonist. The Alliance being an obvious enemy to spy on and kill on sight, and the Horde being allies of necessity rather than ideological compadres, she basically became an antagonist to everyone including the warband she joined. It was an interesting journey as she grew more brutal, murderous and dangerous by the day but still developed unlikely friendships with certain grizzled Orc leaders etc that managed to maintain a bit of... let's call it humanity for lack of a better word. It was interesting, but in the end WoW's RP community turned pretty much even worse than Eve's when it came to consistency and realistic loyalties and so on. If it was inconvenient, it was ignored with zealous determination. Just like in Eve, really, but to an even greater degree.
In New Eden, well... the story is even longer but it resulted in a very different character, even though the core remains the same. It is very interesting to see how Miz has developed very differently from WoWMiz, being a far more authoritarian and "in the open" person than the other incarnation while retaining many of the traits that bind them. The willingness to do what needs to be done for the sake of the cause, even if weaker people aren't willing to, etc.
There's others as well, each having taken different paths ending up as different people and yet they manage to share some core similarities.
I have quite often considered trying to write a metastory where some of them become aware of each other and their connections to a central archetype across realities depending on their particular character's spiritual/mental awareness. Where the most developed of them become able to communicate and draw on each other's strengths and learn from the different lessons and experiences the others have gone through. Perhaps even explore the notion of being aware of the singular mind that first gave birth to them and then pushed them this way or that, and the notion that they still have their own will and so on, expressed in things like how EveMiz doesn't just go with the convenience and take the easy way towards reinvigorating MinFac etc, even though it'd be so much easier for both the character and myself.
I think it's a story that takes a better writer and mind than me to create though.
Anyway, I guess I'm rambling by now and I answered the question in the very first sentence. I roleplay because I can explore how different people act and deal with different settings, and secondarily it lends what is otherwise just mechanically rather boring games (Admit it, MMOs are boring as fuck when you get right down to the mechanics) actual motivation and reasons to go on.