"Little" things as blacksplash details escape some people's minds. However, they matter and make a difference. These days, the traditional 4 inch high backsplash doesn't appeal to everybody. If that's your case, go "fullsplash". Houzz has some fantastic full height backsplash ideas for home improvement junkies - all in tile. Of course, tile is just one of the options, you have glass, metals or more natural stone.
Keep in mind tough that whether you like your backsplash to be 4 inches or 24, definitely do something about covering your drywall. If you like the 4" look that matches your 3/4" thick counters, I recommend using 1/2" thick backsplash. It'll look less "chunky" while still doing the job. Details do make a difference.