Grouting over old grout is an attractive proposition when remodelling a bathroom. Removing old grout can be a painstaking job as it typically involves replacing the odd tile or two. When grouting over old grout, you really have to take the job on a case-by-case basis. A few potential sticking points must be factored in before attempting to put new grout over the top of old grout.
Sealed Versus Unsealed
Sealed grout has a shine to it that resembles the tile. Sealed grout is used in bathrooms and kitchen backsplashes to create a water tight surface and prevent prolonged dampness and mould growth. If your grout has a shine, and water beads up and rolls off of it when wet, you cannot put new grout on top of the old grout. If, however, your grout has a rough appearance, somewhat like cement, the unsealed grout will have a porous enough surface to allow new grout to adhere.
Overall Grout Condition
Depending on the condition of your grout, putting new grout on top of old even if it is unsealed may not be a good idea. Grout is what keeps the tiles together and holds them to your wall. If the old grout is in bad enough shape, with cracking and pieces missing, do not put old grout on top. Your new grout will adhere to the old grout, which is itself tenuously attached to the wall. If your grout is cracking, replace it rather than repair it to prevent further issue.
In any application where water tightness is imperative, as in a shower stall or tile surrounding a tub, you do not want to place new grout on top of old. The outside appearance may be improved, but the lack of a tight bond between grout and tile means there is a better chance of water slipping through. Water behind your tile is a much bigger hassle than grout replacement, so do it once and do it right: remove and replace your old grout.
Often the area around tubs and sinks will have caulk on top of grout. Caulk is a rubbery, typically silicone-based adhesive and sealing agent. New grout will not stick to caulk. If even a small amount of caulk is present on the surface of your old unsealed grout, your new grout will not bond and you will see cracks and grout failure almost immediately. If you think your grout has been caulked, remove and replace it to be safe.