Pale blue, green or yellow on the walls would work fine. You could also paint the walls white, get a white rug, and put up colorful printed curtains, art, and cushions

You might want to think about finding a new coffee table. I think the combination of the couch and big black coffee is too much to achieve a light and cheery look.

My first impulse would be to pair burgundy with green, but if you want the place to be bright, go with a bright blue as your second main color.

Alternatively, do some research on the Moroccan look. That couch would be a great anchor for gorgeous patterned textiles in red, purple, etc. It wouldn't necessarily be cheerful in the way that you might be aiming for, but it would be colorful and fun.

If you had a burgundy blouse - what color skirt would you select to wear with it?

Pink?
Khaki?
Grey?

Then again, there's always slipcovers...

I think a nice pale yellow would work well.

mustard yellow, turquoise, silver.

i also like the idea of a white rug...if you don't have dog.

My son and I just repainted an old house...he had a red couch. We used Sherwin Williams light grey (Big Chill) and it looks great!! Also, I have used a grey-green before which looks terrific with reds, burgundy and pinks. Good luck!!

What about turquoise?

I had a couch in almost the same colour (it had a very retro paisley pattern on it in light pink and aqua though) and my roomate and I painted our walls a pale but really fresh green.
Load up on paint colour chips and start taping them to the walls and see what you gravitate towards! Something will work

Why don't you get a cream or white slipcover for the sofa and then paint the walls whatever color you want.

A soft buttery yellow always achieves and light and cheery feeling and feels fresh. Plus you can pair it with a lot of colors - a soft dove gray for a more modern feel or a nice green or blue in the same tonal range as the yellow. Or keep it clean with crisp black and white.

"What colors go with burgundy besides neutrals? I was hoping to have a cheery and colorful living room,"

Keep the walls bright with a light neutral & cheery with playful accessories. Burgundy is a hard color, but it is quite sophisticated with neutrals. Cheerfulness is about styling too. If that is the couch above, I would slip-cover it. The clean lines & boxy shape means you'll have your choice of brands to choose from. Then you can paint that cheery color you have in mind.

Check out Benjamin Moore's "Westwood Tan". It's a relatively atmospheric shade that can read in the gold, green, tan range. A strong color in upholstery responds well to a definite color on the wall. Anything too pale or pastel could easily look washed out.

I have a couch in a similar color and I painted the walls in light (but not too light) fresh green - similar to the crayola color "inchworm".
I am still amazed how well it matches, the green gives the room a really fresh, cheering atmosphere.

turquoise, purple, pink, orange...

what i would do is:

a. get rid of the coffee table and just have light colored side tables (open rooms help lighten)

b. look into putting a tan or light colored sofa cover

c. either way i think mint, or any light pastel color would lighten up. I personally think a white slipcover with light yellow or light blue walls. then you can accessorize with some bright pillows or decor.

Slip cover it. It's a nice boxy shape and shouldn't prove to be too difficult.

If you're not into slip covers, sage or celery would also brighten up the room. Maybe a green like the color of The Kitchn logo. Some bold pillows and drapes that incorporate both colors in small amounts would tie it all together nicely.

I also failed to mention bold black and white (or ivory).

Some examples:

http://www.ikea.com/us/en/catalog/products/80149064

http://www.ikea.com/us/en/catalog/products/90112017

http://www.ikea.com/us/en/catalog/products/80140756

Lavender.

Light blue!

Take a look at the Pottery Barn catalogue. It's a good place to see colors that work with red and yellow. They work off a 2 color palette - burgundy red and beigey yellow. And then they mix in a variety of greens, blues, and purples each season.

Light golden yellow walls. Patterned sofa pillows with a light (cream?) background and red and yellow in the design (plus other festive colors). Artwork.

Slip covers for openers. If that's not practical, think flower garden brights and go from there. Shasta daisies, roses, tulips. Draw the eye away from the sofa with stripes on the walls or windows. It looks like a good piece of furniture---don't let it throw you off your game.

agreed with some of the previous posts.
mustard yellow or a bright/light blue.
add a few patterned throw pillows and a neutral rug to tie everything in.

I think khaki walls and then get some vibrant pillow and other accessories in Kumquat, burnt orange, jade/blue or citron green. If you can get another coffee table because the black is dragging things down. Thrift a brass and glass table. The add a lamp shade in citron green or a chair-
look here how khaki and the other colors I mentioned work nicely together-
http://www.flickr.com/photos/44713708@N00/3842472205/in/set-72157622103111178/

Or do something like this with a coverlet and cushions and all white walls and table-
http://www.flickr.com/photos/44713708@N00/3842473713/in/set-72157622103111178/
Try to stay away from black, burgundy and grey its going to look very 80's which reminds me of Nagel prints.

Mid-toned gray for walls, curtains with throw pillows with burgundy, cream, camel and gray stripes or pattern. New table in dark brown wood.

I'm kind of tired of seeing all the home design shows with beige and burgundy color schemes...I think gray would be a fresher yet still neutral option.

Or light gray, dark gray, burgundy and white.

Some shade of gray (not too light). Bring in the desired mood with accessories. Green plants will look especially beautiful with these colors. Use pops of ivory (not bright white) here and there, maybe as light fixtures etc to brighten the space.

Burgundy is a beautiful color. I think would look good with layered reds and burnt orange -- and some purple and green. East Indian style. A brass tray coffee table. An oriental style rug and some nice lamps, also eastern style, if possible. I hope you will not leave it at that angle, but will have some nice end tables on either side. And some big floor cushions.

Just for inspiration:
http://www.tribalmonsoon.com/productDetails.asp?CC=49&sbcattt=Wall%20Hanging%20Decor&cat=Decorative%20Pillows%20And%20Accents%20&SC=50a09s48&pcode=57a09s51a09s52&proddesc=Jungle%20Wall%20Tapestry%20Wall%20Hanging%20D%E9cor&activect=1&pro_id=934

http://3.bp.blogspot.com/_PkODtMdz2aI/S31lAjLJHKI/AAAAAAAAArQ/F4zeJLXQCjo/s1600-h/4346005791_a035a20c6e.jpg

I would do jewel tones, and metallics with it.

I agree with Bepsf's suggestion of thinking of the room like an outfit.

Burgundy blouse, charcoal grey skirt, gold accessories, rich purple shoes?

I really hate burgundy with tan and navy. It reminds me of corporate stationery from 1995.

Look to cherry blossoms as inspiration!

Since you want a cheery color, I'd suggest something from color pallet #4 from the color pallet quiz ( http://www.apartmenttherapy.com/chicago/paints-stains-finishes/color-quiz-which-palette-is-which-sherwin-williams-2011-color-forecast-123023 ), though myself I might choose something from #3. The best advice has already been given, and that is it put the room together as you would an outfit.

Benjamin Moore's Adam's Gold is another color that can read gold, green, tan. It looked great with my dark red cabinets.

But personally I'd go with tan/khaki walls, and accessories in burnt orange and bright plum.

I have burgundy as well. I was initially a fighter on colors, but I have found the following to work well:
1) Happy mustard yellow (not the dingy brown dijon color, not the neon ballpark color).
2) Pale avocado. That one was actually the best. You'd think your house would look like candy, but I was in a place with high, high ceilings, so the walls became very neutral.

I have a burgundy sofa, which has purple tones. I painted my walls a light mauve / pink. It looks wonderful! It's important to try out lots of paint shades in samples before you commit to one, as it has to be just right.

Use Google Images to find a _burgundy scarf_ or _burgundy rug_ or _burgandy painting_

You and your roommate each pick your 10 favorites (and hope some overlap.) Look for colors and styles in common.

Also - is it a cool or warm burgundy? Take a clipping to Home Depot and use their paint finder to select matches to your jointly selected wall colors.

Farrow & Ball's Churlish Green, a bright and cheery yellowish-green!

I definitely think orange, pink, or even red would be best. Maybe just the wall behind the couch a bright color and the other walls a light grey or greige with pops of color in pillows, pictures/frames, etc. Good luck!

Light grey on the walls, cushions with some fuchsia on the sofa. Maybe throw a folded black/greay and white piece of fabric on one of the sides.