I have exactly the same problem on my iPhone 3GS with iOS 4.3.3.
But I have iOS 4.3.3 since it came out a few weeks ago. My problem startet yesterday without any obvious event.
Now the symptomps are as follows - ideally you can confirm:
1. Youtube App: crashes immediately
2. Safari App: goes into bookmarks menu, then crashes immediately once I try to open a web page
3. iPod App: goes into playlist menu, then crashes immediately once I try to open a web page
4. App Store App: crashes immediately
5. ITunes App: crashes immediately
6. Mail App: behaves normal in Inbox View, but crashes mostly when trying to open an email
7. Settings>Safari>Clear Cookies: crashes immediately
8. Settings>App Store: crashes immediately
All other native Apple Apps and settings seem to work.
But in this status the iPhone is useless to me.
All attempts to reboot with and without clearing settings before failed. Maybe also because cookie clearing also doesn't work anymore.
Didn't yet restore, but this seems to not be successful either when I read other peoples comments. E.g. here and there (https://discussions.apple.com/thread/3088642).
Need HELP!
Was so happy with the iPhone until yesterday...
PS: my personal fear is that Apple's changes in the background on e.g. the App Store functionality (like viewing and re-loading all previously purchased Apps) are causing this behaviour...