I jumped into the ICQ train kinda late, in 2003, when I was 14. However, I arrived early enough to appreciate it in its full glory, just before everyone switched to the evil, wicked and featureless MSN Messenger.
As I had a dial-up connection back then, I could only spend a few hours (no more than two or three) a week online, so my heart would race and fill with joy at the beautiful sound of a boat's claxon/horn that played at start up.
It's true, as many have said before, that it had loads of useless features and that the interface was pretty messy. But they were useless and messy in a good kind of way. I loved completing my profile, browsing from an endless list of interests and carefully selecting them, knowing deep in my heart that no one would look at them. I also loved the typewriter sound and the oh oh, but I admit I would hate them now.
I met lots of people, most very nice, and some that tried to show me things I hadn't seen before, using the random search function.
Some very good functionality (though I don't know for sure if it was introduced by ICQ), like sending offline messages and saving the chat history were later shamelessly stolen by MSN.
Sadly, ICQ is now a ghost network filled with bots. So I wonder why they still keep on releasing new versions of their client.
Maybe the bots are doing it, or maybe they have hope, as I do, that one day the flower will resurrect from the dead.