They did use glazed ceramic tiles on kitchen walls in 1910, in either black or white, so even if the tiles were a later addition, they wouldn't neccesarily be out of place, or should I say time?
Counters as we know them didn't exist, strictly speaking. Kitchen furniture was pretty much free standing, a cabinet here, a table there. Cabinets and china closets could be built in. Work areas were usually wood, or maybe a marble area for rolling dough. Zinc was used, as was tin, also porcelain enamel.
In other words, any contenporary, durable counter that is pleasing to the eye and looks like it would go nicely with your tile should be acceptable.
You can check out the Victorian and 1920's kitchen albums. You'll see that they started introducing built in cabinets and counters in the 1920's, but the vast majority of kitchens still had that19th c look.
Try just introducing some turn of the century elements into your kitchen design. You might get ideas if you look at the pictures.

Here is a link that might be useful: photo albums

Thanks for the input. I enjoyed the pictures. How about the idea, though, of using the tiled walls as a backsplash? Has anyone ever seen that done?

The tile walls were the ONLY thing I saved in my kitchen (including the floor and the ceiling) that I saved. They work well as a backdrop to the cabinets. My best guess is they are circa 1930:

Oh, wow, Salami, thanks so much for the picture! Your redone kitchen looks great, and this gives me hope for the walls in the kitchen we're redoing. I notice that between the tile walls and the countertop is a strip of wood molding that has a lip on it, which you use for a narrow shelf for spices or whatever. Right? Explain this to me. Also the countertop sort of comes up a bit and the wood is butted against it. What is the material of your countertop--in the picture it looks as if it might be soapstone or granite. It looks very nice, too. Again, thanks a bunch for the picture, and any further explanations of the way you handled this would be most helpful.

Salami, another question: your tile walls look great in the 2nd picture. What did you use to get them so clean and new-looking and to clean the grout???? Thanks again.

The countertops are cast concrete slabs. They were cast upside-down, so there could be an upturned lip at the back of the slab, which meets a small shelf/backsplash made of plywood and solid cherry. This is really to house the outlets, but its nice to have a shelf there too!

The tile required about 10 hours worth of cleaning with a variety of tools and cleansers. Another tricky part was hanging the upper shelves on tile... had to put a 2x4 against the wall with 4" lag bolts and tapcon screws, and then hang the shelves on that.

Thanks again for the answers, salami. One more question: would you mind giving me specific names of various cleaning products? Your cast concrete countertops are great, by the way. I showed DH pix of your "new" kitchen and he could not believe the contrast between before and after.

I really don't remember! was just grabbing whatever I had around... probably a bleach solution, windex, scotch-brite pads, wire brushes... a razor blade scraper is essential for cleaning tiles. good luck!

I just have to say wow - thanks for posting those pictures - and your kitchen is stunning. I have never seen completely tiled walls like that.

I have chartruse and maroon plastic tile as a backsplash halfway up the wall. Much of it has been removed. But I plan to replace it with black and white, esp. now that I know it would be period correct. So on the question of using it as a backsplash, I say, yeah that's what it's for!

I got an italian vapor cleaner and it cleans grout and tile better than anything else that exists. Just happened to post on another thread - you can see a picture of what I bought, and the results it produced on a very dirty floor. I cleaned up my shower grout and tile like nobody's business with it. Very handy for general housecleaning too.

Here is a link that might be useful: scroll down to see the floor I cleaned and my cleaner

For the tile, I've had very good luck with 3M "Trouble Shooter". It's a commercial product; you'd need to get it from a janitorial supply. Spray on, wait 10 minutes, wash off with a scrub pad and water.

You could also use Easy-Off Fume Free oven cleaner, which works pretty well.. I prefer the Trouble Shooter but it is harder to find.