If you have been banned for being blacklisted during the dates of November 13-14 2008, wait a day, and the ban will be removed.
If you are trying to connect to irc.mibbit.com and you are banned with a notice similar to this,
Sindacious[127.0.0.1] (User has been banned from Mibbit ((127.0.0.1) was found blacklisted (DNSBL)))
Then you're connecting to the network with a blacklisted IP address.
What does this mean?
This can mean a number of things, however this normally means the IP address you are using has been used for spamming IRC networks, possibly being used for a open proxy, or your computer is infected with some sort of virus.
But, I'm not doing anything
In the event that you're blacklisted, and you're banned from the server due to this, you can lookup your IP address on the DNS blacklist that you were banned on, and request it is removed. Some will remove it right away, some you have to wait at least 24 hours for the request to be processed.
Where to request for removal
When you're banned form the network you will get a notice looking something like this:
(IP_ADDR) was found blacklisted, see http://njabl.org/cgi-bin/lookup.cgi?query=IP_ADDR
When banned, go to the link that is provided in your ban message, then request for removal after looking up the IP address and seeing the reason why.