You can call the same companies that refinish bathtubs to also refinsh tile. Actually, it's an excellent solution because it also puts the finish over the old grout as well and makes the whole thing not only better looking, but easier to clean.
There are products on the market at your local home center that will (supposedly) allow you to do this yourself. The products are applied like paint. But you will not get the same kind of adhesion with these do-it-yourself solutions. If you want to change these tiles for the long haul, call the in the pros. It's not that expensive.