Devin Townsend's Album Ziltoid the Omniscient is basically a Rock Opera about about the title character destroying the Earth because he gets a bad cup of coffee.
Older Than Radio: J. S. Bach, of all people. Coffee addiction was the moral panic du jour in 18th century Leipzig, so Bach wrote a cantata about it (in favor of the stuff, mind): Schweigt stille, plaudert nicht ("Be still, stop chattering") (BWV 211), better known as the "Coffee cantata." The story concerns a young woman who is in love with coffee. Her father attempts to bribe her out of the habit by promising to find her a husband if she gives it up, to which she agrees. She ends up getting her way after all, by secretly telling her suitors that she will only marry them if they allow her to drink coffee.
The song "Stress" by Jim's Big Ego, as noted at the top of the page. The first half of the first verse he sings about (trying to) cope with his over consumption of caffeine. It doesn't seem to be working, however more alert and attentive it makes him to his work.
A French example — "Un petit café" by Oldelaf. The music video really pulls it off, though. Rather scarily, in fact— the coffee addict becomes Ax-Crazy and eventually dissolves from drinking too much of the stuff.
They Might Be Giants are so devoted to coffee that they actually devoted an entire segment to it in Gigantic: A Tale of Two Johns. Coffee is also mentioned in enough songs that the fan-made wiki chronicles all its mentions in songs. The inevitable result was the band writing and singing several songs promoting Dunkin' Donuts coffee.
The song called "Caffeine" by Taxi is about exactly what you think, and notable for the singer, while graduating with each verse from Coca-Cola to coffee to caffeine pills instead of food, being reduced to unintelligible screaming and gibbering by the song's end.
There's also "The Java Jive", originally by The Ink Spots, but covered by many others (including, oddly, Richard Thompson), since.
Norah Jones has "In the Morning", which sounds like a breakup song, but is really about trying to kick a coffee addiction.
The Anthrax song "Cupajoe" has the singer saying they really need a cup of coffee, go get him a cup of joe. BLACK AND STRONG.
The Beastie Boys mention their fondness for coffee several times, including in Super Disco Breakin' , which starts with the line "Fifty cups of coffee and you know it's on". Coupled with Intergalactic 's claim that "I like my sugar with coffee and cream", one can conclude that the boys' partying lifestyle requires a lot of energy.