What is the process for reformatting SD Card without breaking the current applications on my HTC Incredible?
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.