This is a fun thread. I think I could have picked a better name for it though because I didn't really intend this to necessarily be limited to one or two lines. Hey, we're talking Eagles songs here - in some cases a whole verse may be worthy of inclusion.
In reading everyone's comments, I was thinking that I could probably find a really good lyric in just about everyone of their songs, so I'm going to start at the beginning and post a few at a time that may not have already been mentioned ...
Take It Easy - Heck, this song has so many great lines that we could probably post the entire song, but a few others that stand out to me are the oft quoted "Lighten up while you still can", as well as one of the great double entendres "We may lose and we may win, but we will never be here again, so open up I'm climbin' in".
Witchy Woman - I love the imagery of "A restless spirit on an endless flight", as well as, "She drove herself to madness with a silver spoon", although I had no idea what this one meant for the longest time.
Chug All Night - I think there a few really good lines in this one. My favorite is probably "I'm wired for sound. Are you wired for light?" - very clever.