I first started using phpBB. It was free, my first host would install it for me, and it seemed simple enough. It worked. But I ran into some cookie issues with it. Couldn't stay logged in for some reason. Never could figure it out. So switched to IPB and loved it. Also started a new community w/ MyBB. If it grows and is on an obvious upswing, I'll convert to IPB or vB, but most likely IPB.
phpBB. It lasted for a few hours, then the "love" was gone. Tested a few others I was suggested, and ended up with SMF. I really didn't like the looks of the SMF Core theme, but fortunately there's almost 1500 themes available for SMF. I also like the Babylon theme of SMF, but I don't like the way it's set up.
Ikonboard. Made by Matt Mecham, current developer of IPB. It was a Perl/CGI solution though, but at that time, it was great!
I was quite found of the 2.x series, myself. Still install it on localhost on occasion. Anyway, my very first forum script that I used on my own forum was indeed Woltlab Burning Board 1.1.1.
First forum software I ever used was YaBB SE. Back then, IPB was still free but I didn't really like the look of it, and "everyone" was using phpBB so I got tired of it pretty quick. YaBB SE offered more bbcode tags (this was a big deal to me back then), a nice mod system, and it wasn't as common as the other forum systems.
The very first forum I used was Proboards, I didn't like it so that didn't last very long. I learned on MyBB and later moved to vBulletin 3.0.1 because I moderated a site with vB and liked it a lot.