Bans from Wikipedia are made by the community (e.g. at the Administrators' Noticeboard) or by the Arbitration Committee or by the Wikimedia Foundation (in which case, they are known as the SanFranBan, due to the Foundation's being headquartered in San Francisco).
Scope of bans
Bans can be global, covering all Wikipedias, or limited just to one site (e.g. the English Wikipedia), or limited to one topic (e.g. gender-related topics), or prohibiting only contact with a particular other user (as in the case of an interaction ban).
WP:ANI and talk page
At the Administrators' Noticeboard, the discussions can either be lengthy, or summarily and unilaterally closed, as administrators or others see fit. If an administrator indefinitely blocks a user, and no other administrator unblocks him, then the user is considered effectively banned. Sometimes talk page access is also removed, with the rationale that the user is too dangerous to be allowed to publicly present his case for an unblock, so that the user has no recourse but to file a Unblock Ticket Request System request or email the ArbCom. This means that further proceedings (if any; the request may simply be ignored and the public would never know) will take place privately.
SanFranBans are said to be permanent and not subject to appeal, and there have been no cases of a SanFranBan being officially rescinded. Similarly, although it was common in the past for banned users to be extended a "standard offer" that would allow them to return after six months' absence, and perhaps point to good contributions on other Wikimedia projects as evidence of their reform, what is happening more commonly now is that indeffed users are simply treated as outlaws who are subject to being banned on sight for the rest of their lives, if their editing patterns are recognizable enough to result in a CheckUser.