Because the walls in my building are cinder blocks (fancy, huh?), it's a nightmare attaching anything to a wall, so I need my backsplash to be three things: First, it's gotta be a lean-to, because I can't glue or screw it to the wall; Second, it needs to be a close fit where it meets the hood so it blends into the kitchen without looking conspicuously like an add-on; Third, it needs to be easy (a problem solved by replacing thinset with Loctite Power Grab). Luckily, I noticed that my oven unit has several holes in the back where I managed to use some extra pegboard hangers (those little wire clips that hold tools) to support the completed backsplash. Those clips, plus the tight fit at the top and the inch or so of stove supporting the base, should hold the backsplash pretty nicely. If it starts to come away at the top, using some of that sticky 3M poster gunk should hold it in place without putting any holes in the wall or ripping off the paint.
Finally, and perhaps most importantly, the backsplash needs to look good. It needs to add panache to an otherwise ho-hum area of the wall. It needs to match with our hand towels and the generic tile floor, maybe serve as a visual transition from the beige carpet into a kitchen with a bit of color. It needs to shout Tuscan villa, mid-century modern, and cozy cottage all at the same time. It will serve as the beacon of originality in a The Giver-type dystopia of dullitude and blandification. Reasonable expectations, obviously. A philosophical framework to support you when the caulking gun starts to give your hand blisters and you realize that one of the tiles is obviously larger than the other ones. This is not just a fight for your kitchen, it is a fight for creativity against the blight of apathy and laziness, this is a fight for ALL the kitchens. So suck it up, buttercup, we're making a backsplash.