Here's my scenario:
HTC Incredible, Rooted to MIUI, with an 8GB SD card.
I want to reformat my SD card because I have a ton of junk on it from before I rooted it, so I want to start with a clean install. Since some of the application data is on there, what's the proper process?
I've backed up the SD card by copying all of its contents to a folder on my computer, and I have Titanium backup on my phone for the apps, so I've done those things.
Is it ok to just format the SD card, and let the phone reinstall whatever it needs? Or what's the best way to do this?
Unless you have apps installed on the SD card, nothing on it should be permanent/critical. Any app that always relies on SD data being present is written badly.
There may be some data you want to keep backed up, but that's up to you. It's impossible to say what will happen if you format the card and stick it back in empty, since it depends on every individual app. But generally speaking the apps should continue as if they'd never written anything to the card in the first place. If an app misbehaves then clearing the data should fix it.