It's really bizarre, but one of the most common questions we got from people when we got back was , "did they have toilets?". Strange. I guess people have heard that the bathroom options in Egypt can be...daunting.
FIrst off, don't worry. Egypt has quite modern plumbing. Nearly every place we visited had a western-style toilet -- all the hotels built for the tourists and most places tourist might frequent have a standard flush-toilet of one sort or another. Whether you'll have toilet paper or not is a risk, so carry your own, and be prepared to tip the young woman or young man monitoring the bathroom a pound or so.
Remember that the plumbing (even in high-scale hotels) is probably not prepared to eat lots of toilet paper or feminine products -- don't flush anything down the toilet except a modest amount of paper, if that.
While most places did have toilet paper (out of deference to tourists), many had only a ewer of water or a small spigot next to the toilet for washing off instead. I was a little leery of these in the more remote areas (there is a strong suggestion to not even touch the water of the Nile, and this is surely Nile water), but carrying a little roll of toilet paper and a ziplock bag helped.
We also found at least one bathroom with a porcelain toilet...connected to a hole in the floor. A cup of water was provided to rinse the toilet afterwards. And somewhere on the bank of Thebes is a trailer with a toilet it in...but no back wall. I had a good laugh over that one.
There are definitely a few squat-toilets -- ranging from nicely arrange porcelain footprints in a 'modern" bathroom to a hole in the floor. These really aren't so bad. It's harder for women wearing pants -- you have to either pull them completely out of the way and balance precariously while trying to pee, or pull off one leg and maneuver back into them afterwards. Either is risky, but you get the hang of it.
If you're used to the Chlorox-bleached-sanitized-white bathrooms at home, get over it. Just be prepared -- bring a roll of TP, a little bottle of Purell or other waterless hand-sanitizer, and a zip-lock bag to carry out anything else.