The character can be past or present, but please avoid future characters if possible, unless the appeared in a past show that was set in the future. 
Pick your poison, and state your case. You’re picking the character as they were portrayed in the show, not the actor. So, if you pick Frank Costanza you get Frank Costanza, not Jerry Stiller.
Have fun!
If it was a romantic “move-in”, Emmett from Queer as Folk- while not a brainiac he’s cute, loving, fun and pays his own rent without being whining and grating.
It it’s a straight-up roommates move-in, I’d take Chandler from Friends as he’s responsible, not a druggie (you said the character, not the actor, right?), seems relatively neurosis free and somebody you could trust to pay his rent and leave your stuff alone.
Good thought to include the separate categories. Good call on Chandler too.
/hijack: You wouldn’t happen to be a fan of Dreamland Barbecue would you?/
I love the original (the dirt-road “ribs & bread & chips” place, but the spinoff chains not so much.
I think the android Data, from “Star Trek: The Next Generation,” would make an ideal roommate. He’s neat, he appreciates music, and he likes cats. And, given his (ahem) full functionality, the erotic possibilities are endless.
Damn! 
Oh well, maybe I could take Deanna Troi.
At least she is better looking and will be very understanding when I get jealous and pissy.
But wouldn’t the mind-reading thing be a problem? I’m not sure I could live around someone if I thought she knew what I was thinking.
Yeah but she’d always be coming around going “I know you’re feeling jealous and pissy right now…”. I would hate that in a roomate.
As a matter of fact I think most of the things that might recommend a character as a good roomate (clean, responsible) would just make me feel bad about what a bad (messy, irisponsible) roommate I am. So I’ve decided on Neil, from the Young Ones. First of all while he’s not particualrly neat himself I could get him to do all the housework. Secondly, lentil soup is good for you, I guess. And mostly, because he would always make me feel really good about my life by comparison.
I’ll take Willow from BtVS. No competition for cute guys (they burned that letterman’s jacket, right?), she’s sweeter than sweet but not annoying, and she can make pancakes in shapes. Now that she’s all balancy and white with her magicks, what could go wrong? (I shudder to think what could go wrong in the Jossverse, but this would be in MY universe, right?)
Or Kaylee from Firefly, who’s basically Willow but liking the boys and the machines.
But Deanna is only an empath. She would know that you’re thinking dirty thoughts, but not that they’re about her.
Personally, I could use someone like her in my life. Or maybe her mother. Luwaxanna would be fun to be around, if she don’t drive me insane first. And both of them would know better than to bother me while I’m PMSing, something neither of my current roommates have figured out yet.
The Tick.
Just because. 
Platonic roommate? My choice would have to be Mary Richards (Mary Tyler Moore), – neat, responsible, polite and sensitive to others (albeit to the point of neurosis). Besides,
Romantic roommate? I’d like to move in with Banacek (George Peppard)… nice house, enjoys books, good food and wine… it would work for me.
Kate from Lost. No solid rationale for this, other than that she is incredibly hot and I have a thing for crazy chicks. I would probably end up giving her over to the cops after she knocked over a liquor store, but it would be fun while it lasted.
She’d probably know that I am thinking dirty thoughts about Riker, and she’d kill me.
C.J. Parker from Baywatch.
Come on! A guy has a right to be shallow if he wants to! [hunts in vain for horny, drooling smiley]
Marcia Brady
(have you seen the Very Brady Bunch Movie(think that’s its title)…ROFL!)
Lisa Kudrow- Phoebe from Friends. She’s just yummy.
Elaine from Seinfeld. I love her mannerisms, her sense of humor, her appearance, and pretty much everything about her. Interestingly, I would predict hating her inside three months, but damn that’d be a hot three months.
Alice from the Brady Bunch. C’mon. You’d put up with the bad jokes too for cooking and cleaning.
Ellie May Clampett. Cute, cuddlesome, and richer than Croesus! Someone who would say “Oh, honey! We can’t live in this dump. Let’s buy a mansion somewhere sunny. Here’s money for a few things…will $5,000,000 do?”