I actually think TOR is only 50% MMO - it feels more like KotOR III with optional multiplayer support. And its storylines definitively set it apart from the other games, not just because they are fully voiced and animated. At least *I* am not used to actually being able to influence the way a questline develops or solve a mission in alternate ways. In my opinion, this also makes multiple "playthroughs" more viable, for even if you're visiting the same zone with another class (outside of the separate class quests), you can still have a unique experience by simply solving a problem in a different way. I've purposely created my characters with varying personalities, and it works quite well so far.
Apart from all the slapstick in the Smuggler story, I still think the funniest way I solved an issue was when my character - a female Twi'lek freighter captain with a sorta Indiana Jones'ish behaviour and appearance (minus the hat) - encountered a Sith who was about to kill her if she didn't give up the secret location of a McGuffin. The smuggler, valueing her own hide above anything else, did not have much of a problem complying with this request and feigning alliance. But when a Jedi who hunted the Sith turned up next, she happily went: "Yeah she's gone thataway". Cue a funny encounter between the two Force-users right in front of the treasure, and my smuggler standing ready to cash in once the dust settles.
My most epic experience so far was with my Sith Marauder, though. My Agent, on the other hand, had a story filled with suspense and twists, at times reminding me of a mixture between Casablanca and James Bond.
I'm not just enjoying the stories or occasional roleplaying, though. For me,
PvP is fun as well. Especially with my Smuggler (good healer who isn't afraid to get in close and kick some butt) or my Agent (nasty sniper who prefers to strike from afar), but after some rather frustrating initial experiences I even managed to come up with a viable way to play my Marauder in the warzones.
As with most multiplayer games, however, TOR works best when you have a couple buddies to game with, but this is something the Cave Dweller already mentioned.
I for one do not play it every day, though this is largely influenced by me simply lacking the time. Still, I don't see myself cancelling my sub for another couple months so far. The recent patches have also done much for the game, and considering what more is currently in the works ...
One of my profiles, by the way:
http://wiki.swtor-rp.com/index.php?title=Zana_Tyryn