Cleans (choruses): main, octave below, left/right doubles for impact and usually a harmony left/right doubled.
Screams: main, doubles left/right for impact, layered extra low/high layers in for effect.
I honestly hate double tracked vocals in 90% of situations. With growls/screams I find it to be useless unless the guy needs some thickening up because his voice isn't great and just causes me to have to do a ton more editing to get them perfectly aligned.
With cleans, I only double the main if it's a higher falsetto or something that needs impact, or sometimes when the chorus just needs to be huge sounding.
I edit on the fly for fades/silences/getting rid of mouth noises and stuff, and use VariAudio in cubase for rough pitch correction on the fly (super hard to track harmonies to untuned mains, for instance). I don't need to edit before tracking the doubles as most singers have good relative time (i.e. they're off by the same amount every time) and I'll want to change the timing of the main vocal after we're done tracking (play with push/pull, get syllables grooving properly, generally push the original tracks to be 5-10ms late to pocket better by default)
After the band leaves I go back, remove the vari-audio stuff, comp takes, tune with AutoTune, and then do all the timing alignment and quantizing.
As much as I want to be the guy who edits everything perfectly on the fly, I find that I hit a certain point when tracking where if I spend extra time on editing to make it perfect it kills the session vibe/takes longer than I want to spend while the guy waits, but you can't just leave everything as-is so I try to keep a good balance. I generally have to do my final edits/comping alone, after the session, with a clear head and no distractions. It may take an extra hour after the band leaves every day but it's worth it to me for maintaining good, strong momentum while tracking and still getting a perfectly edited end-result.