Wikipedia has a list of all existing BBS software, sorted by system it ran on here.
I myself used ProBoard and later on PCBoard. I also tried Excalibur BBS later on, but ended up preferring PCBoard.

I started with a 2k4 modem (270 b/s download speed! Wow!), and then upgraded to 14k4, 16k8 (USR!) and later on 19k2 (Zyxel!). I still have my 16k8 US Robotics Courier modems (both ISDN and PSTN). Those modems were considered the nec plus ultra back then and most BBS'es I knew back then ran on those.

*Aaah*, the memories...