It's been done with Star Wars so, as is required by the laws of fandom, it must be done with Star Trek as well.
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This is, yet again, a remix of Call me Maybe, with short snippets of on-screen dialogue (from Next Generation only, mind you!) standing in for Carly Rae Jepsen's vocals. I don't like it as much as the Star Wars one, mostly because it needs to use more single words (which is a little jarring...the Star Wars one had more complete lines), but it's still an impressive achievement.