Does it help if you set Firefox in Offline mode (File > Work Offline) before putting your computer to sleep?

The work offline thing doesn't help.

There's a possibly related tab issue--sometimes if you push ctrl+t to open a new tab after waking from sleep mode, it'll open a blank tab and let you type in the URL bar, but it won't actually show a new tab in your tab bar. It's like a phantom tab or something. If you try to switch tabs, that's when it hangs. It also doesn't load the page fully, especially if there's flash content.

Other times, you can't even open a new "phantom tab", it won't accept any keystrokes. It seems that if you wait a couple minutes after waking from sleep and don't click anything Firefox is more likely to respond to keystrokes.

I haven't ever seen Firefox 8 behave normally after waking from sleep mode, no matter how long I wait. Firefox 7 was fine.

Ok, I got Firefox 8 to respond normally after waking up from sleep. Here's a workaround (I hope a real fix will be coming...):

If you wake up from sleep mode, wait several minutes before clicking ANYTHING in Firefox. No scrolling, no switching tabs, nothing. I waited ~15 minutes while I checked email in my email client (non-Web-based). Then Firefox will magically be responsive again.

Of course, this takes longer than just killing Firefox and reopening it, which is how I'm living with the problem. But this info should hopefully help developers diagnose the issue--there's something about reinitializing the session that takes a while and can't be interrupted or it will hang.