It originally became popular simply due to lack of competition.

AOL Instant Messenger (AIM) was popular but full of ads and didn't offer many features. MSN Messenger (later "Live Messenger" ".Net Messenger Service") didn't exist yet (1999) and while Windows had something called Netmeeting it was simply terrible.

ICQ technically came around before AIM, being released in 1996 Vs. 1997 but AIM hit the ground running as AOL hooked up their massive (then) subscriber base. So while AIM was a more popular service, ICQ became popular with a certain more savvy class of user (e.g. tech' nerds, who wanted more functionality, and something NOT tied to their email address).

ICQ offered that. Less ads, more features, and slightly anonymous (ICQ numbers). ICQ sucks by todays' standards, but in 1996-1999 it was really competing with AIM. There's also Yahoo! Messenger that came out in 1998 which was fairly popular (particularly as an "AIM replacement").

ICQ just somehow remained popular in certain parts of the world for the same reason Facebook isn't going away: It reached a critical mass, now "everyone" is using it which means "everyone" has to continue using it...

Don't forget that the A in AOL stands for 1/193 countries. In AU (yes - anecdote != data) -- friends I would chat with were all on ICQ - before switching over to msn. Never heard of AIM

Second datapoint. In FI everyone who did not use IRC used ICQ and then switched to MSN.

Also AU and used ICQ; then MSN.

Note there was a strong anti-AOL sentiment throughout the 90's.

I used MSN. Now I use XMPP 'cause they wanted me to use skype instead... pffff...

For some reason it was considered anonymous and safe from surveillance.