Based on a 10 day trip to the Red Sea in 2000.
For scubadivers, the Red Sea is paradise. If you don't know how to scubadive, consider taking a course in one of the many diving centers. In case you are unable to go scubadiving for medical reasons, just go snorkeling and you will still be amazed by the beauty of the coral reefs. For some general informaion on the area, visit the Red Sea tourist information website.
We stayed in Dahab which is a great basecamp. It's a nice little resort with tons of great cafes, bars and restaurants directly along the shore where you sit on cushions on the ground and look out on the ocean. The seaside promenade is particularly nice in the evening, with the lights and colours in all those bars giving it a very oriental feel. There is great diving and snorkeling straight from the main beaches in Dahab, and tons of great diving sites in the surrounding area (there are 4WD pickup trucks that take you through the desert to any of those sites). The desert landscapes are also beautiful and the contrast between the immensely colorful world underwater and the barren scenery of the land is just incredible. Don't miss Ras Mohammed National Park, one of the jewels of the Red Sea.
If you need a break from diving, there are some great trips you can take, e.g. to St Katherine Protectorate with its famous monastery and Mount Sinai (make sure you get up early to watch the sunrise from the top of the mountain). There are also some beautiful canyons and oases in the area. Don't forget to go on a camel ride and spend a night camping out in the desert (great stars).