(Edit for Wrath of the Lich King: These guys seem to no longer give weapon skill training.)
Something I discovered during a bugged event in Stormwind about 3 years ago is also of value currently to anyone above about level 55.
In Blasted Lands, in the area around the dark portal, are several "Servant of ..." creatures. They are the objects of a quest in the zone that I've never bothered with. They are interesting however in that WITHOUT the quest, they are essentially immortal. Below 5% health, they go transparent. You cannot bring them below 1%, since you are supposed to shatter a crystal... but you can't do it if not on the quest.
This is useful because you can stand there bashing on them with a variety of weapons and get skillups. Some classes may even be able to AFK the whole fight while training!
Wowhead links are:
Servant of Allistarj
Servant of Grol
Servant of Razelikh
Servant of Sevine