Well that depends on how much you want to spend and what you want to do.
There are free hosted ones. They are simply and easy to setup. But you can not really do much customizing on them.
Then you have paid hosting ones. These can range in price and customization.
Then you can get a hosting account. You will be looking at most likely $10-$20 for a basic account to start off with on the Linux side with a MySQL database. But then you have to get your own forum software.
You want a database drivin forum. The plain text files are slow when they become popular.
I feel there are two main choices in software. vBulletin and phpBB2.
vBulletin you can lease for $80 a year, or buy for $160 and they pay $30 after the first year to keep access to upgrades and stuff like that. I like vBulletin. There is a strong community behind it and is familar to a lot of people. The admin side is awsome and installing most hacks are easy for it.
phpBB2 is free. I don't think it has all the features that vB does but it does seem to have a good community behind it. Where it will go though I have no idea. I think it may take the path of phpNuke and splinter off as it grows and people don't like the direction it is going. But there are people that love it. It is good for the price.