What version of iMovie and what operating system are you using?
Try booting up in Safe Mode (see Finder Help instructions) and, after everything loads, immediately shut down and reboot in normal mode. Sometimes that clears out conflicts that can cause crashes.
You can also try opening iMovie while holding down the Option and Command keys and selecting to delete preferences in the box that appears. iMovie should open in a new library. Hopefully it won't crash. If it opens, then reopen your old library to get back to your projects.
-- Rich