There are three types of forum bans I can think of, and there are ways to evade each.
Username Ban
As a forum administrator, I can ban your user name.
Not much of a problem for you -- you just re-register under another user name.
E-mail Address Ban
As a forum administrator, I can require e-mail address verification to register a username on the forum.
Not much of a problem for you -- you just get a new e-mail account from one of the
free email services and register another user name.
IP Address Ban
As a forum administrator, I can ban the IP address which you appear to come from, or even the range of IP addresses around your current IP address.
This ban is a bit more difficult to avoid, but not much. There are quite a few methods of getting around an IP address ban.
Change your ISP
If you change your ISP, your IP address will change.
Sometimes you can change your IP address by asking your ISP to change it for you, or even by turning off your cable modem or DSL modem and leaving it off for longer than your ISP's DHCP server is configured to remember your MAC address. Or, you can buy a new DSL modem or cable modem and your ISP will see the new MAC address and assign you a new IP address.
Use an Unsecured Wireless Access Point
Another method of avoiding an IP ban is to connect using an unsecured wireless access point. Then, you are using the IP address of that Internet connection.
Use an Anonymous Proxy
Alteratively, you can use an anonymous proxy. You connect to the anonymous proxy and then through the anonymous proxy to the forum.
The forum sees your IP address as being the IP address of the anonymous proxy, not your real IP address.
Use Onion Routing
Onion routing causes your computer to route each connection through another node on the onion network. This causes each of your connections to the forum to appear to come from a different IP address.
Onion routing is usually accomplished using the popular Tor client.
Apologize
Perhaps the best way to avoid a forum ban is to apologize and ask for another chance. This works for all types of bans. E-mail for forum administrator, explain that you understand why you were banned and that you would like another opportunity on the forum.
Most forum administrators really want more forum members, so they are motivated to give you another chance.
If not, there are
plenty of other forums for you out on the Internet.