nerd.nu is among the oldest, public, free Minecraft servers still going. Originally the Reddit public Minecraft server, it's grown into a full gaming community of friends from around the world.
We currently have three nerd.nu Minecraft servers up: PvE - p.nerd.nu; Creative - c.nerd.nu; and Minigames - m.nerd.nu.
... and you can connect to these through your Minecraft client. We don't have many rules, but we ask that you don't attempt to do anything 'cheaty' like x-ray or use flyhacks. Similarly, please don't be trollish by doing anything very obnoxious or offensive.
Come join us and have fun!
I also maintain a few unofficial community resources myself...