The best solution is to eliminate the grout completely. Install stone or solid surface.

That's overkill I think. We use tile and grout on backsplashes because it's fairly easy to clean. Tile and grout on counters is another story, although there are some epoxy grouts that are supposedly simple to clean. Just seal your grout with and you'll be fine, if worse comes to worse, and the grout does yellow overtime and spray on bleach doesn't clean it, there are grout paints that go on easy and color and seal in one step. Your tile should not yellow.

This subject was also in a recent thread. I will link it.

Here is a link that might be useful: Thread about Backsplash behind Range