I'm not aware of the iMovie version you are using, but I've copied and pasted below (with a little editing) two possible solutions that I posted recently in other threads regarding iMovie quitting unexpectedly.
Firstly, trashing iMovie's preference file will often fix problems.
Go to your User (Home) folder Library/Preferences (not the Library folder at the top level in Macintosh HD). Similar to Mountain Lion, on Lion (10.7.4), the User Library folder will be hidden (unlike pre-Lion OS X versions). To access it, click on Go in the Finder menu bar, then press and hold down the Option key - the Library folder will appear in the drop down list, enabling access to it.
In the Library/Preferences folder, locate a file named "com.apple.iMovieApp.plist". With iMovie closed, drag this file to the Desktop. When next opened, iMovie will create a fresh preference file with the default settings. If iMovie now runs OK, you can change these settings in the menu item "IMovie>Preferences" if desired. Also, it's now safe to drag the old preference file to the Trash. Trashing the file will not harm your existing Events or Projects.
Secondly, if trashing iMovie's preference file does not fix the problem, you may need to delete one or more third party QuickTime components (as recommended by others in various threads). Some components have been known to cause conflicts with iMovie, particularly if they are older versions that have not been updated to work with current Mac OS X systems.
The component that seems to be causing the most trouble for users is "3ivxVideoCodec.component" (which possibly is associated with installed Flip MinoHD camera software). Two recent iMovie updates (9.0.7 and 9.0.8) did address the issue of incompatible components and should have fixed this. However, have a look in the folder "Macintosh HD/Library/QuickTime" and check if you have the 3ivx component. If so, drag it to the Desktop then see if iMovie opens and works OK.
You may also need to remove other third party components from the QuickTime folder. But don't remove the following two Apple components: "AppleIntermediateCodec.component" and "AppleMPEG2Codec.component".
By a process of elimination, you should be able to isolate the component (or components) that may be causing a problem with iMovie. Remove each one in turn, then try running iMovie. Hopefully you will find the culprit! Trash (or update) any components that are causing problems and drag all others back to the QuickTime folder.
John