OK, thoughts for dealing with yucky white grout. (BTDT)
1) Futurebeachbum has a good suggestion. If it is yucky but not too yucky I use Clorox Clean up (gel if you can find it, otherwise spray) and a good stiff bristle brush. Detergent plus bleach can work wonders. IF you can get it satisfactorally white, then seal it with AquaMix's Sealers Choice Gold or 511 Porous Plus. :clap_1: Several coats until you are done.
2) If you can't get it white and you really want it white, then consider using one of those grout paints from the Brookstone catalog. I think they are some sort of epoxy paint. You MUST prep the grout exactly as instructed first, but if you do it right it will last a long time. I used it over dark yucky OLD grout in a bathroom in our first home and it turned out great, and was still looking great 3 years later when we sold it. Tedious but worth it if you don't have mosaic tile.
3) Finally, consider a grout colorant. In our beach house bathrooms we have white hex tile. The very optimistic (or careless) builders used white grout.

:bicycle: :nono1:
After awhile of course it was not cleanable, so the only solution was to color it with a more traditional medium grey. I got all my (high quality) supplies from Lowes. To do it quickly on hex tile I followed some instructions by the guys at the John Bridge Tile forum, which is the best. I've done two of the three bathrooms and they look great! Next time up I'll do the master bathroom, which is bigger so it will take longer.
One good thing about the colorant, in addition to the fact that it evens the grout color and makes it look "clean," is that it also is a sealer so you don't have to worry about doing it ever again!