There have been many reports here of issues with Aperture crashing after the Aperture 3.4 upgrade. Some reported fixing it by reinstalling the app, while others reported it fixed by trashing the preferences.
For those of you that trashed the preferences — your fix is only temporary. You will need to reinstall the app. Just delete it and re-download from the App store.
If you bought it on DVD and have been upgrading all along, then you’ll need to reinstall from the disc again and upgrade. So be sure you know where that DVD is before proceeding!
For anyone upgrading now (i.e. haven’t upgraded to 3.4 yet) you shouldn’t run into the problem at all.
Apple has a complete article on how to reinstall here: Aperture 3.4: May quit unexpectedly on launch after updating.