One of my pet peeves with kitchen backsplashes is this side backsplash hanging way up in mid-air for no apparent reason. This is a bad detail. You see it in many builder homes and it's primarily the tile guy just making a decision on the job site of where to stop and start the tile.
The only reason to have a side backsplash like this is if there is a water source close by where the wall will get repeated dousing on a regular basis. Of course the other reason is if the countertop installer was not very good and didn't scribe the counter to the wall so that a tight joint sealed with a small caulking is impossible. Many contractors use this side backsplash to "cover" the large gap between the counter and the wall. Even if the wall is uneven or is tight at one place and wide at another, a good countertop installer should be able to cut the counters to butt tightly to the wall.
If you MUST have a side backsplash for any of the above reasons, make sure the tile is the color of the wall so that visually it doesn't call attention to itself and please use either a tumbled tile with a rounded edge, or get the tile guy to bullnose the edge pieces for a finished look.
Perfect bullnosing of the tile at the unfinished edge.
Otherwise....DON'T do it! My basic rule (which sometimes has to be broken) is to always try to die two different finishes in an inside corner. See how this works with backsplashes?
One of my "Before" kitchen remodels. See the backsplash on the left hanging in mid-air?
"After" - See how there is no need for a backsplash on the far left and how neat and tidy it looks?
I don't have many hard and fast "rules" that I use, but this is definitely one of them.