The first flavor is "short term," which means you did something stupid enough to earn you a vacation from the forum, but nothin so bad you need a permament ban. These run anywhere from a day to a matter of months. Smurfing to revisit will turn it into a permanent ban. (aka suspension, a time out)
The second flavor is "indefinite." It means you've done enough, crossed enough lines, or irritated the mods enough that you're banned until we think it's time for you to come back. Constantly asking about when you can come back will not help your case. Smurfing to revisit will turn it into a permanent ban.
The third flavor is "permanent." That means you're gone, for good, kthxbye. Smurfing to revisit will do you no favors and has the potential to bring about legal action against you. So don't go there. Take the hint and move on without us; there's nothing here that's so important you need to make a nuisance of yourself and/or take that risk.
You can appeal any ban if you think it's unjust by writing Fry or the mods, but if you choose to do this, do so calmly, maturely, and be ready to apologize if you were in the wrong. That won't guarantee you a trip back, but being a jerk will guarantee you *won't* get back in. Constantly asking or, god forbid, harassing mods over it will be futile.