A warm earthy beige, similar to the walls in these posts:
http://www.apartmenttherapy.com/chicago/good-questions/does-this-warm-wall-color-work-good-questions-111219

http://www.apartmenttherapy.com/ny/good-questions/good-questions-what-color-sofa-should-we-get-for-the-living-room-030501

http://www.apartmenttherapy.com/dc/the-power-of-accessories-3-looks-for-one-beige-room-country-living--128860

I'd say a light gray. would make it look bigger. It'd look nice with the white and compliment the existing countertops (which look charcoal to me.)

I would skip the paint and maybe focus on modern wood and glossy light grey cabinets.

http://luxury-kitchens.homes-interior.com/2010/05/10/wood-kitchens-design.html

Strip your cabinets and treat them with grey lye soap and the appropriate oil. It's a Danish product -- Wocca I believe.

white always looks nice with blue and will make the floor pop and will modernize the space if you put brushed chrome handles on the doors/drawers as well

White.

Woca is the name of the company. Either white or grey lye would look amazing!

Matte finishes are now just starting to come into vogue in North America, and look fresher and more natural than high gloss finishes.

Please, NO handles. It looks neater and less fussy if you don't add them. A white solid surface counter (Corian or marble) would be beautiful though.

It already looks good, surprisingly so since I wouldn't have thought blue tiles would look that nice in a kitchen. Would you please post after photos later?

White cabinets would complement the blue floors nicely! Consider light gray paint for the walls (I like Benjamin Moore's Stonington Gray). I painted my kitchen that color and every said it looked bigger!

White, white white! It will look so clean and pretty, maybe with a mid-tone grey on the walls.

Why not a wooden laminated floor (easy to install and to clean and cheap)? Colors for kitchen can be from neutral classic (white, cream, gray, lavender) or strong bold colors. With the black top I'd choose a neutral tone if you don't plan to change it. If you do, I'd choose lavender or olive green and cream-light gray-white top.
(from an interior designer actually living in China!)

PS: a darker color for walls and different one for ceiling

Watery, watery blue to pick up the lightest tone in the tile. Then paint the cabinets a butter or butter cream colour instead of stark white. Adding a really nice handle to all the cabinets in say, brushed nickel, will add a nice finishing touch.

Definitely paint the cabinets white. And I think a nice gray on the wall would be lovely. I've been doing a lot with deep blue lately as we just painted our master bedroom blue so here are some inspiration blue room pics I've been storing on pinterest if it helps you think of color schemes: http://pinterest.com/shunta/home-inspiration/

White cabinets and a butter yellow on the walls.

We rented a place with cabinets that were blue, I painted the walls butter yellow, looked amazing and it was always bright and fresh.

And paint whatever of the appliances you can or switch them out. There's stainless steel paint out there, or one blogger used this and said it worked great: Krylon Metallic Leafing and Smoke Gray mixed.

Well, I guess I'll be the odd woman out. I think plain jane grey on the walls with white cabinets would be a bit boring. I'm ok with the idea of white cabinets, but why not put a little color on the walls? I have the same blue tiles in my entryway and cobalt blue tiles in my shower - they are definitely challenging to work around. I'm into the greenish yellow shades with that color of blue. It pops. These are the three colors I liked best in that range, but they may be brighter than what you're looking for (though it'll give you a jumping off point to look for other shades): Valspar's Almond Puff, Valspar's Golden Avocado and Benjamin Moore's Eve Green. If you wanted a bit more of a monochromatic look with the white cabinets (and it's gorgeous with pops of yellow or fuchsia or lime accents), Benjamin Moore makes a fabulous greyed-violet-blue called Blue Nova. It's in my top 5 of favorite, versatile colors. The plus is that that color went on super easy for us, practically one coat on whitish walls. It's a little dark, but if you go white with the cabinets I don't think it would be too heavy - you'll have quite a bit of white to balance against it. It would look lovely with some butcher block countertops too. Hope this helps!

Well, I would definitely paint the cabinets a warm white and the walls a pale grey/blue I think. Also, you should really consider selling your appliances and putting money towards a nice stainless set....the black is not good with the blue tile and the pop of stainless would really make the kitchen look more expensive and the floor will seem more deliberate.

Really interesting floor color....

A combination of modern stainless steel, orange and white..... The ratio of the parts depend on what you have in mind...

My parents have blue tile in their kitchen. Their walls and cabinets are ivory and the window trims are a sage green. The lightness of the walls opens up the room.

Tile all walls -- backsplash, walls -- with a patterned blue and white tile, either Spanish porcelain or ceramic or a Moroccan or Cuban cement tile.

Here are some ideas:

http://www.aventetile.com/portfolio/155.cfm?startrow=1

http://www.luxetile.com/hand_painted_ceramics_tiles.aspx

I'm a big fan of Dunn Edwards Champagne color, which blends beautifully with the blue tile in my kitchen, bathroom and fireplace surround. It's a buttery color that can morph from wheat to peach, depending on the time of day and light.

If this were me, I would go for darker cabinets on the bottom and lighter cabinets on top. Especially with those dark appliances.

So you are in a predicament which struck my curiosity so I went on behr.com to see what they would match the blue and black with (the only elements you can't change). Of course, I found some unexpected results. My favorite was ash white and a deep smokey blueish/purple.

Point being, really check this out on their website. You can even slap the paint on a virtual room and see how it looks.

Grey and white, or grey and a light blue might work.

Think about the colors in with Delft Blue or Flowblue pottery.

I like the idea of white cabinets and appliances (use appliance paint). I might also paint the countertop (Rustoleum have new products to do both cabinets and laminate countertops). I would paint the cabinets and walls first, then decide if the countertops work or not.

The suggestions for buttery yellow on the walls would work great - really making that cobalt pop out even more.

Find some Moorish/ Spanish/ Portuguese/ Italian/ Mexican etc. tiles (or other ceramic piece) that you love and that goes with the floor (and counter and appliances, if you are keeping them). Pick the colorscheme for wall & cabinets from the tiles (or whatever).

Using the tiles as focal pieces in a backsplash that's mostly white/cream etc. will make the backsplash reasonably inexpensive.

Or, find a textile that goes with the floor - either a curtain fabric if you have windows in the space, or pretty dishtowels or apron, whatever - and pull your color scheme from that.

I would suggest a light celedon green. It'll play with the warmth of the cabinets and has some blue to work with the floor. It also looks fab with black appliances. No need to change everything out.

White cabinets with a pale grey wall color would be beautiful and then you can do any accent color you want with accessories and switch those out over time when you need a new look. Good Luck!

Go nautical. Paint the walls pure white. Strip and dye the cabinets as suggested by mschateleine to a pale grey. Blue and white wide vertical striped roman shade in heavy canvas could be added. I don't see what lighting fixture you have on the ceiling but a galley lantern or apothecary lantern would fit with a nautical style. Just don't overdo it. You don't want to live in a theme park..

I like the idea of the lye soap which would allow the natural wood to remain but would lighten it up. I am starting to get tired of seeing white cabinets everywhere.

I don't know what your style is, but knowing you like the floor and using it as a jumping off point, I would...
Leave or refinish the cabs and go with Mexican talavera-style tile on the countertops and fun ceramic knobs like these: http://www.tierrayfuego.com/Ceramic-Tile/santa-barbara-tile-ceramic-door-knobs.html

Or go ahead and paint the cabs white, leave the counters, and use the knobs I linked for a hint of talavera and to make the floors look intentional.

If I were you I would replace the mini backsplash with a real one, the mini does look a bit dated (in my opinion). White cabinets and grey walls seem to be a popular choice and I have to say I like it too!

These all great ideas and can wait to get paint samples and start getting the ball rolling. I did just recently install bronze fixtures (they were $2 for 12pk knobs and there are a lot of cabinets! couldn't beat the deal!) I also found a black pendant fixture (modern looking for $30) with all the diy ideas on AT I could easily change it up if needed. I love everyone's ideas and can't wait to play around with your ideas! I really don't have a specific design I like, which makes this even more challenging! look for a before/after soon! thank you everyone!