If your bathroom tile has started to look a little funky with age, you can rejuvenate it without a complete overhaul. Sometimes, as they get old, a fine film covers the tiles. To clear it away, rub the tiles with a mixture that's one part muriatic acid to five parts water, then immediately dry it with a cloth.
Now, what about that grungy grout? First try bleaching it, using an old toothbrush as an applicator. If that fails, then consider staining it a dark color, using grout stain (in a pinch, you can also use shingle stain to get your desired color.) Or, if you insist on white grout, try carefully scraping away the top layer with a small flat blade, then applying a tile sealer to keep it white longer.