what color is the tile? my sil had unsealed tan grout on tan tile and spilled grape juice!!!! The next best avenue was to stain the entire shebang...they vacuumed and mopped the entire floor and once dry they went over the grout lines with boiled linseed oil...looks good, no more stains.
+1 on vinegar. Got the suggestions from this board several months back. Had been using Sun Oxygen cleaner before than (which worked pretty well), but the vinegar is simple, cheap, and works as well or better.
I just thought about this one...we have dark green grout and a bottle of CLR that one of the kids brought from college leaked on it and completely bleached out the green!
Muriatic Acid. We used it on every job for washing stone and grout. You just have to cut it at 32 to 1 for grout, 16 or 8 to 1 for stone. Wear gloves and goggles.
I worked for my Dad between semesters in college doing commercial stone work. We used about 20 gallons of muriatic acid on the federal courthouse floors in Denver.