Thieves
The term "thief" can cover anyone from the drunken thug who beats a beggar for his alms, to the merchants who smuggle kidnapped children to sell to southern slave dealers, to the sophisticated burglar who slips in and out of a merchant's townhouse. Despite what one might think, it is rare for thieves to work alone. While anyone can snatch a purse here or there, only those who work in groups can really make a living from it.
Thieves' Guilds
Thieves' guilds gather like-minded individuals who make alliances, plan jobs, and get information on buildings, people and security measures. Being part of a thieves' guild provides the same basic benefits as any other guild: insurance, training, and tricks of the trade. Members get access to specialized equipment and information to make their job easier. If a member of the guild gets into legal trouble, the guild may be able to pull some strings and arrange their release, though the member will likely have to reinburse the guild for its trouble.
Another benefit of guild membership is more sophisticated thievery. A guild allows for such things as protection rackets, where people pay the thieves' guild to insure they, their homes and their buildings are not burgled. This only works with the cooperation of guild members, of course. If a merchant pays protection money but they are robbed anyway, they are not likely to pay again. This is the main reason why independent thieves are not tolerated within a guild's territory--not only are they not paying the guild its fair share of the loot, but they could irreperably damage the guild's reputation.
Thieves' guilds also build up a repetoire of snitches, informants, bribed officials, and magic connections that other guild members may use. Smuggling goods, either for direct profit or through fencing, is also easier when thieves work together. The officials may catch one or two thieves, but the operation goes on.
Although a strong leader might occasionally unite various factions of thieves into a single guild, it is more common for multiple guilds to stake out territory throughout the city. The Black Hands claim gambling and girl rights in the docks ward, and the Unseen claim pick pocketing and begging on Baker St, for example. Turf wars are not at all uncommon, especially among the smaller and more volatile guilds (which are little more than gangs).
(It might be more helpful to think of mafia and Russian mob movies for inspiration, rather than fantasy thief guilds.)
Relationship With Other Factions
Thieves are almost universally disliked by other factions, who will nonetheless hire them when necessary. Theft and burglary are considered serious crimes, usually punished by branding and mutilation. Theft of Church property is dealt with even more harshly.
Although the Hermetic Order does not have any official connection to thieves' guilds, many mages are known to sell potions and spells to thieves through the black market.
Misconceptions
Thieves guilds are not large. A small guild would have only a handful of members, and even the largest would have less than a few dozen. Thieves are generally too shifty and selfish to create extended organizations.
Most thieves are not highly sophisticated burglars; brutish thugs and smugglers are far more common.
