I am so tired of having to empty my dehumidifier every day and I don't have a basement drain. Does anyone know if a window unit exists?

Do you have a sump pump in the basement that you could drain it to?

I did some googling, and see window dehumidifiers referred to fairly frequently (http://www.google.com/search?hl=en&q=%22window+dehumidifier%22&btnG=Google+Search) but struck out on finding someone who sells them.

Since they're mentioned, though, it's worth continuing to search, but an option you might consider if you can't find one is to put a small pump (http://www.google.com/search?hl=en&q=mini+sump+pump&btnG=Google+Search) in the dehumidifiers reservoir to pump it out the window. Yes, it's a bit "rube goldberg" but it would work in a pinch.

Well, any window air conditioner will also be a dehumidifier, and those will drain to the outside. I cannot think of many reasons you would mount a dehumidifier in a window and not want the air conditioning effect as well. It basically comes for free, as a dehumidifier is an air conditioner that vents the hot exhaust back into the same room (instead of venting outside).

Well, any window air conditioner will also be a dehumidifier...

This will not work. The A/C unit will dehumidify only when cooling. For more, see here:
http://www.misterfixit.com/dehumifaq1.htm