Is there a directory for public servers?
Solution 1:
There is no official directory for Minecraft servers, but the most popular places are:
Minecraft Classic Servers
Minecraft Alpha Servers
Solution 2:
The official Minecraft forums encourage people to list their SMP servers.
Also, anyone running MCAdmin with the server list option turned on will appear in this list. if it's in there it's almost certainly public.
Solution 3:
There is also Abyssal-Legion Minecraft Server Status Page.