A great way to visit Egypt without being part of a tour is to hire a guide (150-200 LE/day) and a taxi w/ a driver (120LE/day) for the day.  It's a great service, for not much money and you can go where you want, when you want.  The guides will help you at the sites and monuments, find good koshari restaurants, take you where you want, etc.  It's a very inexpensive way to visit Cairo and Luxor and it is great not to be on the rushed schedule of the tour buses.

Prices for guides and taxis are up now (2008) and you will need more than 200 LE/day for a guide and more than 120 LE/day for a taxi. Book your guide through a certified agent in Cairo/Luxor/etc so that you a sure you get what you pay for.