A few shirts have personal value as parts of interesting sets of clothing, or as proof of obtaining a rare drop or rare quest, but most are considered junk to non-roleplayers.
Most shirts do not bind at all and may be purchased from vendors, other players, or the Auction House. There are seven Bind on Pickup (BOP) shirts that are available to both factions but one is only conjured during a boss fight.
The [Precious's Ribbon] is the only uncommon quality shirt that exists in the game. It is also the only available shirt to feature an equip action that puts a buff on the character. The buff reads "Best in Show".
Mists of Pandaria may include more uncommon quality shirts for guilds, if the Beta is any indication.
The [Martin Fury] was the only artifact quality shirt that exists in the game. It was a Game Master shirt and players only got it by mistake. If you ever got this, you needed to report it to a game master or you would get permanently banned like Karatechop from Vek'nilash US. At some point it became a poor item.