Each character class has an ongoing main quest that is more or less single-player RPG main storyline quality, and which spans the entirety of levels 1-50. If anything, I've enjoyed some of them more than single-player RPG storylines, because most of the class quests avoid the awful "you are the Chosen One who is destined to do X" cliché. That's probably because you can't have a million Chosen Ones running around, but I'd argue that it actually led to more interesting storytelling, by allowing the writers to focus on what a Republic soldier or an Imperial spy would actually do in the Star Wars universe. (Most of the non-class quests are straightforward collect-10-bear-asses fare, but usually with a storytelling hook or twist to keep them somewhat interesting. They're definitely not on the same level as the main quest, however, and can get tedious.)
That said, I'm interested in the game solely for the same reason you are--I have little interest in Star Wars and a pretty low opinion of the MMORPG genre--and I played it for ~50 hours during the beta weekends without boredom or disappointment. I don't know if it's something I'll be playing six or twelve months down the road, but right now it's as close to a good Bioware RPG as we've got.