You are not a jukebox, you are a DJ, which means you have been hired by someone to curate a soundscape of agreeable music for the night. Not only is playing a bad request an amateur move, it establishes you as a DJ who people know they can manipulate into being a jukebox.
If someone wants to hear a track in the style that you’re presently playing, it’s a good look to be accommodating, but by the same token, if you’ve got a packed dancefloor going in to some bass music and somebody demands to hear “Thriller” immediately (a request that is oh-so real), you deserve to have your equipment smashed for accommodating that request. Part of being a quality DJ means getting the crowd to trust your music choice, and while it’s vital you read the crowd and learn what they want to hear, bowing to every request you get is a quick road to obscurity, not to mention a great way to kill any mood you've been building.
Be as polite as you can, but be firm—say NO to bad requests and don’t even bother with negotiating, as that just takes your attention further away from your job. Accept that some people will understand, but most won’t, and they very well might feel like being an asshole about it. Keep in mind that this is their problem, not yours, especially if you’ve got the club going up on a school night. And if you’ve really gotta tell someone off, we’ve always been partial to telling jokers to “go buy an iPod.”