In my present kitchen I have no tiles and the backsplash wall is painted. It's fine. I think (but not an expert) that you should caulk between the granite edge and the wall. It will keep the water from getting behind your cabinets. You can use clear kitchen caulk.

Yes, as Pam said, you need to seal the edges so that stuff doesn't run down behind. There should be wet area drywall behind, and you can use wet area paint. Or you can go choose tile. Or put up something temporary just in the sink area.

The fact is, you do have a backsplash. The wall behind the sink and stove and counter is a backsplash. It's a back and it gets splashed. I haven't been cooking long in my new kitchen, and prep mostly on the island, but I've splashed the back plenty. ;)

Wallpaper works, too. I'm sticking with my white paint for now. When I get tired of that look I'll do something else. I had planned on subway but with the matte white counter I didn't like the shiny subway. I haven't found a matte subway here so can't see it in person.

We didn't put in a tiled or granite backsplash b/c we postponed it due to budget (plus I didn't know what I wanted). We just painted w/a scrubbable paint (BM Cornsilk).

However, be sure you tell the templater that you will not have a backsplash...and keep telling him/her! Otherwise, they'll assume they don't have do that good a job of templating along the wall b/c they'll think the tile will hide it. Oh, and put it in writing!

Even though I was very explicit and they had our design with NO backsplash, they still gave me a gap that was big enough to push my fingers in up to my knuckles...I refused to sign off until they fixed it. I now have a fairly small gap that black silicone (or is it caulk?) hides very well and also keeps water (and crumbs) from falling behind the counters.

I have a black counter, so the black is perfect. There is one run that has clear and we tried painting over, but the paint doesn't "stick"...so make sure they use something that either already matches your counter or wall or that can be painted.

We're not planning a backsplash and one of our big inspirations was trailrunners kitchen. I don't know if they ever mentioned what they did, but you might try searching for it.

And heed the wise words of buehl. There is a base assumption that counters and walls don't need to meet cleanly because the backsplash will cover it.