I have been working on several projects on linux and am comsidering making them open source. I used the Qt window library, I really like it espacialy compared to MFC, and was wondering if most users would be able to compile and run my programs. I belive Qt is required to run KDE so I am Guessing that KDE users could, but what about gnome or iceWM people.

They can compile it, but unless you have the trolltech license ($$$) you will not be able to sell it. But you mentioned opensource, which is great.

Also, QT apps will run fine under other desktop environments. Only the QT libraries are needed, not all of KDE, and these are usually already installed. To compile users might need to install some extra development stuff, but that shouldn't be too much of a problem and you wouldn't get around it with another toolkit anyways.