Lots of what was said in the poll is important, but another thing I NEED to here in my music is power and muscle. I hate it when bands rip out all the sound from their music, making it wimpy and boring (you know, sorta like Linkin Park...). I have a different take on lyrics as other people have said here. I don't mind much if I can't understand a songs words at first, because usually I eventually will. For instance, I used to only be able to pick out some of the words in "The Spy Hunter" by Project 86, but my musical tastes got heavier and heavier, and not only do I now know all the lyrics to it by heart, but it's one of my favorite songs by them ("Safe Haven" takes the top spot though for all-time fave). When I do read and understznd those words, though, they have to be intelligent, deep, creative, and meaningful. I WANT it to take some thinking to fully understand the meaning. To me, usually if I can understand a song by just reading through it like I would a book, then I see that as a lack of creativity. That's a major reason why Project 86 fans like me dig them so much: They combine powerful music with equally awesome lyrics.
Oh, and before someone beats me to the punch...
"Na-na's, hey-heys, and doot-doos do NOT count as legit lyrics." --