All apps and system software are up to date.... (4-3-13).
Are you using iPhoto '11 or an earlier version? Your profile signature says Mac OS X (10.6.7)?
When did this problem start? After importing new photos? After an iPhoto crash?
If it happened after importing new images, you may have imported a bad image file or video. Then I'd suggest to remove your last import from your iPhoto library.
If the problem followed a crash, probably your iPhoto Library needs repairing, or you are running out of disk space.
How much free disk space do you have?
- If it is less than 10 GB free space, I'd suggest to make space on your start up drive by deleting unnecessary files as soon as possible
- To repair or rebuild your iPhoto Library, see: iPhoto 6 and later: Rebuilding the iPhoto library
- If the built-in ⌥⌘ Library First Aid Tools don't help, try to rebuild the Library with iPhoto Library Manager, see Old Toad's Post here (Fix 2):
Added: To answer your original question: Deleting the iPhoto application and reinstalling will not delete your imported photos. It is perfectly save, but still, it is necessary to make a backup, before you install/ reinstall any software.
iPhoto keeps the imported image files in your iPhoto library - that is stored in your "Pictures" folder by default. See Terence devlin's User Tip: How to Access Files in iPhoto