Moment You Definitely Have To Imitate: Going as low as you possibly can on "I hang my head and cry" in "Folsom Prison Blues," regardless of the obvious strain on your voice and how terribly it comes out.
Bonus Tip: It's essentially impossible to sing Johnny Cash well. As long as you're comfortable with that, go for it!
Moment You Definitely Have To Imitate: The crazy, emotional nonsense at the end of "With Or Without You". Make sure to do this during any instrumental breaks in any U2 songs, even if it's not actually there and even if no one else is around.
Bonus Tip: Anytime you see a camera, grab it and get up to it real close and pretend to eat it. Then be like "But seriously, Africa." People will be like "I guess you mean well." Also have a cowboy hat sometimes.
Moment You Definitely Have To Imitate: Just make sure to throw multiple overly-emphasized Michael Jackson-ey "AH!"s "OOH!"s and "NAH!"s throughout every song (and you get one "SHAM-ON", so use it wisely)
Bonus Tip: Don't try to dance unless you're amazingly good or obviously-hilariously-bad. Anything in between is excruciating.
Moment You Definitely Have To Imitate: You have to sing "You" as "Yeeeeuuuuuuuw" in "Like A Rolling Stone". Bonus Tip: The more absurdly "Stock Dylan Impression"-ey you sound, the more accurate it somehow becomes. (Click the pic below to play, because the song somehow isn't on Youtube -- more like The Freewheelin-ly LITIGIOUS Bob Dylan):
Moment You Definitely Have To Imitate: The verses in "Even Flow" (Fast, tonal gibberish, punctuated by alternating "oh yeah"s and "all right"s. Then make up for it on the word BUTTERFLIES.)
Bonus Tip: Just do the same voice for Creed, if you're singing along to them for some reason.
Honorable Mentions: Prince, The Bee Gees, Billy Joe Armstrong, Elvis, Rob Thomas, Louis Armstrong, Adam Duritz, Every 80s Metal Singer. Others? Leave 'em in the comments!