It is understandable that Americans, and others, might want to listen to the State Department and leave Cairo in a hurry, but there is an alternative, which is to stay in Cairo and watch history unfold. These demonstrations are directed against one person; they are not directed against Americans, or any other national group. Here's proof, from Israeli tour guide Amos Abidov:
"The attitude towards us as Israelis and tourist is very friendly. Actually, they're overly nice compared to my previous visits in Egypt. The Egyptians want to explain themselves, to tell everyone about their struggle. They speak Arabic over here so it's easy to communicate with them. On Friday we went right past the demonstrations on our way back from the pyramids, and people helped us get though the crowd."
The first instinct, to run from these situations, isn't always the best instinct. This doesn't mean people shouldn't be cautious and alert for mood changes, but often there is little reason to run away like mice.