Albums, and the order I bought them in:
Best of 1980-1990
October
War
The Unforgettable Fire
Under A Blood Red Sky
Rattle & Hum
Achtung Baby
Pop
Zooropa
The Joshua Tree
Boy
The Joshua Tree (first copy got scratched due to so many listens)
Passengers
The Joshua Tree (second copy got stolen because, of course, it is so amazing)
All That You Can't Leave Behind
Best of 1990-2000
How To Dismantle An Atomic Bomb
First song I heard by U2: Hold Me Thrill Me Kiss Me Kill Me at age 13 when watching Batman Forever after buying it long after its release; my mind was blown and has continued to be blown ever since.
Fan since the Batman Forever viewing in 1997. Serious fan starting with the purchase of the Best of 1980-1990, which first I listened to over and over at a friend's house.