Could be a number of things. Is it just the one file, or is it all of them?
1. Could be a corrupt file. Check out Adobe's site for recovery information.
2. Could be an incorrect file extension. For example, you may have saved an eps with a .ai extension, an Illustrator file with a .eps extension, or maybe used no extension at all. Although it should still open anyway, OSX does rely on file extensions much more than previous versions of MacOS. Maybe it's getting confused!
3. Try opening the file from Illustrator's File > Open... dialog box, rather than just double-clicking it.
4. If it's an EPS, try creating a new document and using File > Place... to add your file to it.
5. If you have Distiller, try creating a PDF from your file. You might be able to open this.
6. Maybe Illustrator itself is at fault. Try reinstalling.