Login to another user account on your Mac. If you don't have one, go to System Preferences > Accounts
Click + to add a new account. If the + is grayed out, click the gold padlock icon to make changes. You will be prompted for your admin password.
Then click +
When you see Name type Test. Create a password then click Create Account.
Now login to that account. Try Safari. If Safari crashes in that account also, then it's likely the startup disk needs repairing.
If that is the case, launch Disk Utility located in Applications > Utilities
Select MactintoshHD on the left then select the First Aid tab.
Then click: Verify Disk (Not Verify Disk Permissions)
If the disk needs repairing, click Repair Disk.
Make Safari crash, then open Console & look at the log messages.
You may see something like crashdump: crash report written to: /Users/XXXX/Library/Logs/CrashReporter/Safari.crash.log
or you can look directly in that Folder using Finder to see if there's anything recent.