I've been using white tires for a long time and have never had too much trouble with them looking "grungy". They're obviously not going to stay as bright as when new but under pretty normal riding conditions, I've found them to be just fine (and I never clean them except for a quick wipe when cleaning my bike). I suppose they do wear a little quicker but I don't skid, so even that's never been any sort of problem.
I do agree with Retro Grouch though. White bars/black grips and white rims/black tires will look classy as all hell.