I have used grout paint on mine with a toothbrush to apply. It's sold at all the big box home improvement stores.
I've used an abundant number of products but best for me for thorough clean tiles/grout around bath and shower cubicle is neat bleach...
Wear gloves, apply neat bleach with a large sponge or cloth (cheap one), scrub stubborn marks with an old toothbrush or nailbrush (so you can get into grout areas), leave for 10-20 minutes and rinse thoroughly with cold water.
You may want to visit your local Lowes or Home Depot and visit the rental center and ask for Klean-Strip 1-Gal. Green Safer Muriatic Acid it works great on tile grout cleaning when scrubbed with hot water. It's also safe for anybody living in the house. It is your easiest fix. Visit http://www.remodelinghomeimprovement.net for other green remodeling ideas, tips and tricks.
Check out this article I wrote.
One point I like to point out to clients when working on tile projects is the "appropriate" grout color choice. White should never really be used in any floor type of setting, the work needed to keep it white will be a full time job. When we tiled our cabins floor we actually took a sample of the soil there and picked a grout color that matched it. In our case that happened to be Tobacco brown.
If you want to have new looking grout again or change the color check out my sealer www.groutshields.com if you have any questions just call were here to help
I've used 1/3 bleach 2/3 water - apply to the grout with a spray bottle (wear old pants) then scrub with grout brush/ and wipe with damp cloth....has worked great for me, plus your house smells clean afterwards :)
Try plain old Hydrogen Peroxide, I use an old syringe to put it on
the grout lines, let it set and bubble as long as you think it needs.