I like the gray color 3rd one out from the backsplash. I think its a great color...very versatile, doesn't compete with your punchy tile backsplash and can be a great background for showcasing art in the living area. I would stay away from green or any color with a green undertone. Good luck and please post pics after you've painted!

what about something with a little more blue -- the glassy green backsplash would really pop on blue.. whereas a neutral might try and blend with it making it seem like you're trying to hide it

What about black? Here's what it might look like:

http://www.flickr.com/photos/51096455@N00/2212453086/

red

red is good

Sorry, but I think the gray would be awful. Pretty much the worst choice. If you love the impact of the back-splash, I would take the intensity of that element out to the rest of the room--in other words, don't think that you're going to somehow balance that intensity by doing something subtle. You'll accomplish just the opposite: No balance at all. You should consider doing a color that is just as intense. If you can handle it, a striking apple red would be amazing. If you want something just as dramatic but not quite as glam, do a very intense chocolate brown.

I'd use a greyish lavender.

Don't go green -- green is legendarily impossible to match just right, and a sage like you have in the paint is fundamentally different from the kind of spring green you have in the tile.

I'm finding the beige most similar to the cabinets as the best of the options on your wall, though I'm not surprised to hear recommendations of gray. Try for a gray with a yellow undertone, not a blue undertone.

I'd go with beige, too. Or maybe khaki.

I don't think gray would be awful at all. Or is it grey? Either way, it is a good color choice for a subtle option.

I like the black as well if you want something more striking.

Red seems like you'll be celebrating Christmas all year long!

Deck the kitchen with boughs of holly....

second the blue suggestion.

what about using black chalkboard paint? you get the drama of black, with the moodiness of grey, and the abiltity to write friend's drunken comments....i mean..grocery lists on your wall

a soft orange or yellow-orange.

paint it the same color as the grout between the tiles.

I think a rich blue would be the best choice; it will pull together the dark appliances and the green glass tile.
Go to Benjamin Moore's website for a look at their "virtual fan deck", and click on the blue/green section of the deck.
I found several......bermuda blue, seaport blue, toronto blue, laguna blue, deep ocean, naples blue. If you choose a semi-gloss for the wall(and usually I don't), it will reflect light in a manner similar to glass. Buy a quart of one of these colors, cover at least 24 square inches, and watch how it changes with the light in the room. Ralph Lauren: Blue Island, Montego Bay, or Aegean Blue(to the green side of the spectrum) are some specific samples I have on hand.

a yellow-toned off-white.

I'm surprised that you haven't given thought to a darker purple color for the green. My girlfriend begged me to do a purple in our dining room when we moved in together and I was surprised at how much I liked the color we picked out together. From the looks of things, I think you are trying to go too neutral, when what would really complement that kind of green is another vivid color.

Good luck with everything!

Pale gray.

Chocolate brown looks great against those shades of green and it will also compliment the "neutral off white color" of your living room.

I like the idea of chocolate brown. Maybe even aqua? I'm not much for a lot of bright color, but I do agree that something more muted might just make the back splash seem out of place and not necessarily "feature" it in the way you're looking for.

Third the idea of chocolate brown. It will make the green pop. Or go with another dark saturated neutral, something in the way of Benjamin Moore's "Thyme" or "Golden Meadow." Have fun . . . the end result will be STUNNING!

I vote for the yellowish color that you have on the wall that is abutting the green tiles near the microwave. Its a nice happy color and it will work well with living room color.

I vote for gray! In fact I've seen a kitchen backsplash tiled in different yellow, green, black, and gray tiles that looked awesome.

I have two wall colors... chartreuse and pale, pale blue.

I think you should play with blues.

Poor Nat . . . you're probably even more confused now than before our helpful suggestions.
Go with your gut--if you don't love it, paint it again!

Benjamin Moore Sweet Pear, if you want a similar tone to the backsplash or BM Blue Angel for a light blue contrasting color or BM Grappa would provide a moody counterpoint.

I second wendeinphoenix's choice of the beige that matches the cabinets. Lets the tile "pop" without the cabinet competing. And you could do some accent colors with art or tea towels or something on the wall in between...

Thanks everyone for your very helpful comments. I have a lot to think about. There were some very interesting suggestions as I expected.

http://www.wnetwork.com/tv_shows/shows/colour_confidential/episodes/epi_71/before_after.asp

Check out this link. It's from a canadian show called "Colour Confidential" and I just watched this episode last night. It's hard to see in the photo but the backsplash is a soft green with some bright green glass tiles inserted in a row. They painted some of the interiors of the cabinets green and they painted all the pine cabinets gray.

Might just be the gray you are looking for.

what about a very very soft pink, something just a hint, like from farrow and ball?