ImageJ is one of the older free, open source image analysis programs. Alone, it's not that powerful; it's real strength is the vast array of plugins for it. It runs on Windows, Mac, and Linux.
FIJI is probably the best distribution of ImageJ for routine data analysis. It comes with a vast array of plugins already installed and ready to use (including the three mentioned below) and has an automatic updater so you always have the latest versions of them.
Micro-Manager is a microscope control package that is built on top of ImageJ. It's developed at UCSF and is very powerful; we use it to control the Spinning Disk Confocal in the Nikon Imaging Center.
A tutorial on getting started with micro-manager: http://www.youtube.com/watch?v=y-R9WmhzPdI&feature=related
A screen cast tutorial on multi dimensional acquisition using micro-manager: http://www.youtube.com/watch?v=6LoKX6Eect0
The following plugins may be of particular interest to NIC users:
ICS Opener - Allows ImageJ to open ICS files from the Nikon C1 confocal.
ND2 Reader - Opens NIS-Elements ND2 files (old, may be outdated).
Bioformats - Library for reading many microscopy file types, including ICS and ND2. Probably preferred to the ND2 reader above.
If you do a lot of work with ImageJ, you may want to subscribe to the ImageJ mailing list: http://rsbweb.nih.gov/ij/list.html