My mother has stainless steel square tiles over her range. They were there when she bought the house. They look great, not too shiny. They are laid so that the "grain" on the tiles alternates - so it makes sort of a checkerboard pattern with the sheens - if that makes sense. She's lived with them for 3 years and is happy with them and they always look clean.

I actually installed a small wall of these tiles in my son's kitchen. The major problem with these tiles is when they were cut (using a wet saw) they had very sharp edges which needed to be filed down, so they were actually more work than any of the other backsplash tiles I've ever worked with. Once you file down the edges they look nice, but they are hollow once cut and you'll definitely need some sort of border on any open ended walls. You could break apart the tiles from the mesh and use individual tiles vertically as a border.

Helene

Well, it sounds encouraging. I think shininess will be an ever- changing thing, depending on the time of day and the light, which in itself is kind of interesting. I had read about how sharp the edges get when you cut them and the need to file them down. This is beyond my skill set, so if I buy them at Lowe's I'll ask about having them installed and make sure it's someone who has done them before. Most of it will between counter and cabinet, but on each side there is a space with just wall above. Cutting some tiles to make a border might work, but I'll keep searching to see if there are any matching or at least coordinating bullnose or other type of border. If not, it might just turn out to be grout or caulk.

For the area with no cabinets above it perhaps you could use one of the Schluter edge profiles. It comes in 8 ft lengths and can be cut to the length you need. So you should be able to get the open areas of your tile done with just one strip of the trim.
I used their Jolly profile in the satin nickel finish on the vertical edges of my mosaic tile.

I don't think the Jolly comes in stainless but it is available in polished nickel which may be a close enough match. Not all big box stores carry all finishes but you may be able to order the finish you want or check with local tile stores.

Schluter has another edge called the Quadec. It is a wider profile than what I used but it does come in stainless. My sister used it in her bathroom and it looks good. This picture of the Quadec edge is from the Schluter website

If you have a Costco nearby, also check there. They had SS subway tiles the other day that looked really nice.

The Costco SS subway tile looks really great. Looks like gray grout. Badgergirl I will definitely check out the Quadec and the Jolly. The one with the brown tile looks perfect, but I wonder what the Jolly would look like.
Next question is should I wait until all the painting is done?

I've posted this pic before, but it's Martha Stewart in her studio kitchen for the show "Martha Stewart's Cooking School". I believe it is a stainless steel sheet behind her range. I think the sheet is then embossed to look like tile; with a sheet you wouldn't have to worry about grout. I don't know the source of her stainless sheet, but either check her website, write to her show, or just google for a stainless steel sheet backsplash that looks like tile.

We seriously considered stainless tile for our backsplash (we ended up with small crackle tiles just because I thought we had too much stainless already). It'll look great. Just wanted you to know Schluter is super easy to work with - we trimmed out both bathrooms with Schluter, and also used it under the kitchen cabinets (which have no lip) to hide the LED strip lights.

Wow! That trim on the underside of the cabinet looks fantastic. That just might work for trimming the subway tiles.

We are in the process of installing that exact look, only we went with a local tile shop and got it a few dollars cheaper per sq ft and it is a superior quality product then what we saw at home depot. It came with a protective film over the front of the tile to protect it while installing it. We are having trouble with the black grout we got going light gray an we don't know how to fix it yet.

Laying the tile went perfectly though. One thing we did that saved a lot of trouble was we bought a sheet of the 2x2" SS tiles to fill in the edges instead of having to cut half tiles. We only had to actually cut a handful of tiles for the inside corner of the backsplash and for a few electrical outlets, but all of these cuts will be covered by outlet covers and by the next row of tiles in the case of the corner. It looks awesome (except for our grout problems)