Look at that chinatown house tour / color entry for inspiration - they had lots of bright red. I think they paired it with light blue and lemon-lime.

i love bright red with turqouise. try jamaica blue by benjamin moore

i would paint the walls a very pale shade of grey - with a little bit of red added to warmth.

A sunny but somewhat earthy yellow? That's my answer to everything, though. ;D

I agree with OneWallKitchen, but in a much broader sense. A sunny but somewhat earthy yellow just might be the answer to most problems. (Metaphorically speaking.)

Apple Green

I think because the sofa is so bright and stands out it would fight with the walls if they were bright as well.

My suggestion would be: Blustery Wind By Dunn Edwards.
(DE6304)

Paint the walls yellow on top and orange on the bottom, like in this painting:

http://www.allposters.com/-sp/Number-5-Posters_i378854_.htm

~Q

I had thought of lime green/apple green, but I also agree with kristian's suggestion of turquoise. I think either would look great!

Or you could paint 3 of the walls chocolate brown, and just paint the wall behind the couch in green or turquoise. (Maybe that would be too much color on the one wall? Paint the wall opposite the couch in the accent color?)

I would do a gray. I did our guest room in Benjamin Moore 'Silver Fox', and have a black leather chair and other accents (pillows, artwork) in that shade of red and I really like the way it turned out.

seems like you could have a real color disaster on your hands after this post. I agree with jenc and tamara and pkswede if you want to keep it sophisticated.

If you want to go nuts...GO NUTS! Paint every wall a different color, drop some acid, stand back and watch the magic ;) Good luck.

White or Light Gray. There are some very nice pale grays at Restoration Hardware.

SHIMMER from Devine Paints. It's a BEAUTIFUL shade of beige that really pics up anything in the red/orange family. Check out the swatches.

I have a fanatical love of red/brown, which can be splashed with either peach or yellow.

Blues and greens are on the opposite ends of the color wheel from red so if you put the 2 together they fight with each other. Have you seen a sign with red letters on a bright blue or green background? They sort of flash back and forth. I think your red sofa in such a small space is your shock of color. Perhaps you should paint the walls in a neutral just as some others here have suggested. Then add colorful artwork to tie in the sofa.

A pale taupe or warm stone grey -- like a river stone.

"Blues and greens are on the opposite ends of the color wheel from red so if you put the 2 together they fight with each other."

That's ridiculous.
Do Red Roses "fight" with their green stems and leaves or the blue sky? Of course not!

The OP asked for something dramatic - whites and beiges are anything but dramatic.

I think the point is the HUE of the color. Green and blue can work but if its a strong blue and a strong green, not so much...maybe as accents, more likely. There are certainly flowers in nature that are purple, yellow, pink and green. Put them in a room together and it looks like Miami threw up on you. Personally, if you want drama, and you have a red couch...the couch is the drama, which you can play up with strong bold fabric curtains, pillows carpets...but the walls, my vote is for a more subtle hue of one of the many colors suggested so far. Color is very subjective as is taste and style. Sky's the limit. If you want to know what will "Work" with your red sofa, I think there are some viable options listed.

Oh thank you, bepsf. I gave my opinion. You don't have to like it nor do you have to be so condescending.

i also vote for the pale gray

Thanks to you all for great ideas! I definitely want to avoid having Miami throwing up in our guest room (love the image, though)--thanks to JenC for pointing me to the Chinatown color contest slideshow--I think I am sold on some kind of pale springy green. Check out this great red/green combo: http://gallery.apartmenttherapy.com/photo/111307dan/05_redlockers

Saplet - I was going to say the spring green also! Love that or the robin's egg blue idea...or both!

I think white will be right. I think anytime you have a red object with a white background, it gives off a very museum vibe.

I just painted a very similar room (small guest room w/ red sofa) with BM gray cashmere and love it.