Archie, X.500, ftp, gopher, telnet, irc, mailing lists, USENET, WAIS, WWW (remember to use WWW clients), a caching WWW server for Funet members, Alex ("Global filesystem for all anonymous ftp sites with caching (experimental)")
You could telnet into the system with username info and use command-line clients for some of these services if you didn't have access at your home university.
I vaguely remember using an email-based service to access web pages: you sent the URL to an address and got a reply with the page contents rendered as text. That probably wasn't Funet but something else.
ftp.hornet.org for early demoscene downloads.
of course never forget ftp.simtel.net. My shareware apps I releases in the 90’s are still there somewhere :)
Unfortunately also university servers retire, and with them we lose the digital history they contain. Shout out to funet.fi and archive.org for taking good care of old files!