I've been trying to find some new bands to listen to, but haven't really been successful in finding something I really like in this particular category.
Dark, spacey, and kinda trippy is good (though doesn't necessarily have to be constantly slow paced). Radiohead and Smashing Pumpkin's Adore album are examples of what I likes.

If anything comes to mind, name it! New, old, whatever. :]

I cant' really vouch for them, but my friend really likes The Birthday Massacre. I don't know, I'm not really up on the music scene anymore, so you may already know about them and have ruled them out. But they seem to fit many of the criteria you listed.

Dark:
-Jack Off Jill
-Murder By Death?
-Dead Poetic
-The Dresden Dolls
-Evanescence
-My Chemical Romance

Spacey:
?

Trippy:
-MGMT
-Fight Like Apes


All of the above: None

You might like Silversun Pickups. They match up fairly well with Radiohead and Smashing Pumpkins. Actually, if you go into Shoegazer music (Silversun Pickups, Lush, Magnetic Morning, My Bloody Valentine), you might find a bunch you like. It's super slow paced tho...

I can't help but think 'The Gathering' would be right up your alley. Try the album 'If Then Else' if you're interested.

Or, if you prefer more experimental, nothing beats 'Godspeed You Black Emperor!'.

I like 'Tool' and 'A Perfect Circle', although with the latter you're going to want to see which is the cover or heavy antiwar political albums.

'Evanescence' is good if you stick with the first album. The second one is mostly pop music.

For trippy, try 'The Avalanches' or 'Boards of Canada'.

dude...i'm tired of telling people this. Fallen is the second album. Open Door is the 3rd. Open Door isn't horrible like people like to think either. Definitely the first 2 Evanescence albums tho. Give the 3rd a listen if you so choose.

Maybe Jeff Buckley? 30 seconds to mars? Pendulum?

For trippy, you can't go wrong with Blue Man Group.

For dark/epic music, I've always been a fan of E.S. Posthumous. ...Within Temptation is also pretty good.

Maybe not what your lookin' for, but...

On the Gothy side, Swans:



On the metal side, Neurosis:

Yes! Download the albums, Yes, Virginia and No, Virginia.

Honourable Mentions:
Sex Changes; Sing; Dear Jenny

When I hear dark, spacey, and trippy, I think of Archive and Portishead immediately. Boards of Canada might not be a bad way to go if you don't mind instrumental music.
Home Video is awesome, it's kind of like if Thom Yorke's solo album was slightly danceable. Early Clinic (namely Internal Wrangler and Walking With Thee), Slint's album Spiderland, Moderat (download their song Rusty Nails at least, I think it's their best), and um... that's all I can think of at the moment.

Buck-Tick is a pretty cool band and his mid-to-late 90's period meets the criteria that you're looking for (perhaps some songs are a little bit The Cure-ish). However, don't know how you feel about J-rock...

Maybe STS9 might be your thing. But they are more electronic than spacey or trippy.

EDIT: oh yeah they aren't dark at all so probably not what you're looking for.