Are there any known cases of courts issuing an exclusion order or any
similar decision banning a person from entering an Internet forum, in
the US or abroad?
I am seeking specifically cases involving someone repeatedly
interrupting the forum’s regular course of business.

Dear Tomash, 

I remembered this 2000 story of a 14-year-old who pumped junk stocks
through news groups :
http://www.latticefinancial.com/stockmarketefficiency.html (but he
also committed other crimes).

In general, the authority of the moderator to ban someone out of a
forum is protected in its disclaimer or terms of service.

See a discussion on the question in a gaming forum:
http://batse.com/online/chess3/1951.shtml

I have read that during July 2000 eBay has asked a federal judge in
Chicago to remove a user (Braxton Anderson) from its Web site for
harassing users and staff. Court decisions on this case and similar
cases are exactly what I'm looking for (preferably concerning forums).
Thanx.

The only helpful reference to the Anderson case (aside from news
reports) was found here:
Applying "Freedom of Association" Laws to Cyberspace By Stan Morris -
http://www.gigalaw.com/articles/2000-all/morris-2000-08-all.html