I was playing Half-Life while listening to Simon and Garfunkel (a weird combination, I know) on Windows Media Player, when I noticed that the song was actually being played twice, with about a one second delay between the two. So I switched out and cancelled the Media Player, only to find that somehow Half-Life had associated the CD's music with its own sound files (and restarting Half-Life didn't stop it). Having "Here's to you, Mrs. Robinson" play the entire time I was on the Xen homeworld produced a rather different atmosphere than I'm used to in that area.
So, what are the strangest glitches you guys have ever had in your games?