Notifications that exist as of today (June 11th 2012):
- earned a badge
- veteran users don't get all of these
- earned a new privilege
- these are suppressed when creating an account
- bounty completed
- bounty expires in 3 days
- bounty expires in 24 hours
- got association bonus
- the "welcome!" message
- an election has started (nomination phase)
- an election has moved into the primaries
- voting has started in an election
- a post was migrated
- an edit was suggested on a post
- on SO only, a new reply was added to a moderator message chain
- obviously, only moderators see these
- everywhere else these are put in the inbox
- even on SO, if a moderator has participated in the chain these go into their inbox
- a non-trivial* edit was made to a post
For a while before the new notifications tab was enabled the old "big orange" messages were going into it verbatim behind the scenes. A number of those messages won't be sent anymore, but we didn't (and won't be, obviously) delete the old ones.
* a non-trivial edit is one which changes at least 10 characters (this is using a diff algorithm, so it's not a simple add/delete; and is naturally a little fuzzy). For the "technical" sites (where code highlighting is enabled) changes to code of at least 2 characters are considered non-trivial.