I personally LOVE that shade of green in the flowers... I would paint that color. If your afraid of too much color then make that color a feature wall and find a much more subdued shade of that green or white for the rest...

I would look for a pale mint green (not too blue-ey or it will clash with the neon green on the bedspread) or maybe a lavendar.

If you want something sort of neutral, a pale gray would be nice.If you're going for color, do a bright pink!

Gold like that side table in the picture. But only for an accent wall. If you have high ceilings, I would only paint 7 or 8ft up the wall and then give top it off with simple molding.

I agree with: Benjamin Moore "Country Comfort" is a gorgeous, rich but muted yellow suggested by medusa12120.

I'm not a fan of grey walls but a cool grey might work too. Just remember the size of the room and what the color may do to change the look.

Chartreuse (the flower color) will brighten your basement.

A nice light gray, baby blue, or creamy yellow. I would go with white trim for any of those colors though.

Something in the range of Orange/Peach/Goldenrod

pick something not in the bedding like royal blue or even black don't worry it will be so cool looking and with the right lighting very cozy.

id go with sico serene blue. would be perfect. + i love this color so much!

When pulling a color from a print I usually go with the smallest element. In your example I would pull that olive green that lies buried in the chartreuse. It would highlight the pink, and as green is the complementary color of the red range, it would work as well with the pinky brown in the coverlet.

go to http://colorschemedesigner.com/ you can enter in the colors from the bedding and it will spit out the perfect complementary color for you!

Sherwin Williams "celery" is a yellowy green, but not as neon as the duvet

My first thought is to pick up the hot pink/geranium color in the flowers.

If that's too much, then use the brown/taupe tone.

I dislike green on a personal level. You also risk your room looking like a hospital.

A dark teal or marine blue, like BM's Tuscon Teal:
http://www.benjaminmoore.com/en-us/paint-color/tucsonteal

I completely agree about a blue colour - if you were considering an accent wall, I would even suggest a kind of turquoise (a similar shade to the pink in your duvet, but in blue). That would probably be too much for all four walls, but could be an interesting splash of colour.

I'd consider what other colors you have in your apartment. It might be good to have a palette of colors that work well together (compliment, not match) as people frequently experience many rooms at once (with doors open, etc).

I'd also be wary of anything too peachy. I have used the color scheme design tool that Tffnynelson mentioned with great results (OK, it was for my website, but still...). I bet if you played around with it, you'd find something you really like.Like this.

This would be stunning against olive!

Do NOT pick a shade based on the bedding (yellows, pinks, greens, etc.), otherwise you'll be locking yourself down with that bedding, or ones that feel similar. As we all know, tastes change, and should one day you decide you want bright red bedding, it's going to look really strange against that chartreuse that you might have picked because it matched the original duvet. With that said, definitely go for a neutral. I think grey is always a wise choice, keeping it on the lighter side since you don't get too much light!

I would use a light blue or kind of turquoise

My first thought was pink, but I like the suggestions of light blue and turquoise.

Agree with the subdued version of the chartreuse team. I love Benjamin Moore "pale avocado" and it would work great--or maybe even the next lightest on that paint card. If you get tired of the bedding, it will still work with lots of other colours/patterns.

Olive would be too drab for a basement, I think.

I think it would look awesome with dark gray walls - like a warm charcoal color. That said, I would hesitate against planning the whole room around the bedding because I have had some UO bedding in the past and it is not made to last. Then again, it's not like you'll never be able to find other bedding that will go with your wall colors, no matter what you pick, so if this bedding is your inspiration point then maybe just go for it.

I agree with the few that have suggested pulling out that olive green, but my spin on it would be that I'd do a paint color that's a bit more neutral than outright olive... maybe Benjamin Moore's Home on the Range?

Go BOLD with a chartreuse accent wall behind the bed and then do the other walls in a beige-y peachy color to keep things bright. Dark walls in a basement are going to feel cavernous!

I also love Benjamin Moore "Country Comfort" It would go really well with the bedding and brighten up the room a bit.

Peacock blue. Wouldn't match, but would set off the colours in the bedding brilliantly.

Benjamin Moore Espresso Bean behind the bed, and Snow White (or a milk white shade) every where else. Make sure to have good lighting on that wall.

It will be dramatic and cozy, and yet not overly cave-like. (although I have no idea what your apartment is like, so am working on a number of assumptions).

OOOO! I'm thinking PERIWINKLE!

Given the colours in that bedding... hot pink would be kinda awesome!

I want that same duvet cover and have been looking at it on UO! My bedroom I just painted a very pale grey that is on the cooler side of the color scale. I think it would look awesome in the room. I have canvas curtains made from a drop cloth so it is kind of a greyish-putty color and I am adding a bright pink ball fringe to it. So many choices!

Something that isn't matchy would look great. I have a 70's floral print couch with some crazy colors in it and the wall behind it is Sherwin Williams Silvermist. On chips it looks much more grey than it is, it's a very neutral, light blue color. I normally wouldn't choose something like it, but I love it so much I would ALMOST put it in every room.