1. A muddy, swampy area that is hard to traverse.
2. A situation, often political/military, that's difficult to get out of. The building casualties and increased length of occupation in Iraq give one example.
3. Peter Griffin's sex-crazed and very loose next door neighbor on the show "Family Guy." A former Navy man, now a commercial pilot. Catchphrases include "Giggidy giggidy giggidy" and "Oh!" (accompanied by a thrusting motion with the arms)
"George W. Bush is actually quite talented. He managed to create a quagmire in a dry desert."
Host: Who else but Quagmire?
Song: He's Quagmire! Quagmire! You never really know what he's gonna do next, he's Quagmire! Quagmire!
Quagmire: Giggidy giggidy giggidy giggidy let's have sex!
Peter: Alright Cleveland, if this doesn't light a fire in your belly, nothing will. puts on a mask of Quagmire's face
Hey, look at me, I'm Quagmire! I had sex with your wife! Giggidy giggidy giggidy giggidy!
Cleveland: Hahaha! Those are so his mannerisms!