My goodness, I have way too many favorites to count, because these guys are just too good at what they do. A couple off the top of my head that I love for some reason or another... Sorry for the wall of text in advance!
-"It may be raining / but there's a rainbow above you" is so strangely hopeful to me.
-The whole call-and-response bit in the Desperado/DD reprise - especially "You sealed your fate up a long time ago / now there's no time left to borrow"
-"Beauty in the devil's disguise" and "All this gratification and sick conversation / someone get me outta town" from Good Day In Hell
-I've always love, love, loved "You know I've always been a dreamer, spent my life runnin' round / And it's so hard to change, can't seem to settle down" from TITTL.
-Every lyric in HC is pure genius, let's be real. Favorites include "Some dance to remember, some dance to forget" and the steely knives line because I am a sucker for references. I love how the lyrics have literally painted the same mental picture of "The Hotel California" and its inherent debauchery for me since childhood.
-"We've been up and down this highway, haven't seen a goddamn thing" from LITFL. Along with a couple of the lines central to the meaning of the song that 7 year old me did NOT get the meanings of until much later, like "Lines on the mirror, lines on her face".
-Wasted Time is a goldmine of favorite lyrics for me, but one that's always stuck with me has been "The autumn leaves have got you thinking about the first time that you fell / you didn't love the boy too much, no no you just loved the boy too well".
-"Tell all your girlfriends, your been around the world friends, that talk is for losers and fools" is a great one from my fav Eagles song of all time, Victim Of Love.
-"Hi there, how are ya, been a long time / seems like we've come a long way" is one from PMAIAR that I always seem to remember at Eagles shows... Kinda reminds me that even if I go a while without listening to the boys, they're always there to bring me right back to a state of happiness, like old friends!
-The Last Resort. So, so many in this one. "Where the old world shadows hang heavy in the air" is a favorite because of the stellar imagery it provides for me. The last verses after the key change (one of my favorite key changes ever) are all some of my favorite examples of amazing songwriting from this band, not to mention Don's delivery of those lyrics give me chills every time.
-"I don't know why fortune smiles on some and lets the rest go free" is a GREAT one from Sad Cafe.
-So many great lyrics in Get Over It. But my favorites are "Don't wanna work, you wanna live like a king, but the big bad world doesn't owe you a thing" and "I'd like to find your inner child and kick its little ass". Basically all the lyrics, actually. GOI is my "screw you, world" song.
-From Learn To Be Still, "one more starry-eyed messiah meets a violent farewell". I also kind of want just the phrase "learn to be still" as a tattoo eventually somewhere because I love that phrase/song so much.
-From Hole In The World, "They say that anger is just love disappointed / they say that love is just a state of mind". (Random side note... could that be a throwback to Stevie Nicks/Fleetwood Mac? "Dreams unwind, love's a state of mind" from the very end of Rhiannon... Hmmmm..... Am I the only one who's noticed that??)
-"If finding love is just a dance, proximity and chance / you will excuse me if I skip the masquerade" from WITW
-Really, really love the "And we pray to our lord, who we know is American" verses from Frail Grasp. So delightfully, sardonically, politically Henley.
-And lastly, there are SO many in LROOE. But I especially love "Captains of the old order clinging to the reins, assuring us these aches inside are only growing pains" and the last line "All the knowledge in the world is of no use to fools, and it's a long road out of Eden."
This is just a partial list, since EVERY Eagles song has a line or two I really like above all the others. But these are the ones I especially love.