The rogueclass has a trained ability, [Pick Lock], which allows them to open locked items. This can be learned at level 20 from any rogue trainer. Lockpicking skill is 5 times the rogue's level.
Blacksmiths can craft skeleton keys which are able to open locks of different levels. Each recipe yields multiple keys which can only be used by blacksmiths with the appropriate blacksmithing skill. The keys are consumed after successfully lockpicking an object.
Engineers can craft Seaforium Charges which provide a similar function to skeleton keys. Only engineers with the appropriate engineering skill can use the charges. The charges are consumed after successfully lockpicking an object.
The Scarlet Crusade of Tyr's Hand in the Eastern Plaguelands have many lockboxes that will challenge your skill.
If you can't unlock an item yourself, you will need to rely upon the lockpicking services of a rogue, blacksmith, or engineer to do it for you. When approaching a lockpicker, keep the following in mind:
You should only open a trade window with a lockpicker if they are publicly advertising their lockpicking services or you have already asked them in a whisper. It is not acceptable to simply open a trade with someone in the hope they will open your item, as they may be busy with auctions or mail, and your trade request could disrupt them.
Even if a lockpicker offers their services for "free," they may still expect a tip. There are no set guidelines for what constitutes an acceptable tip. Tips may vary depending on the type of lockbox, the number of boxes needing to be unlocked, the value of the items found inside the lockbox, cost of materials (for blacksmiths and engineers), the wealth of the tipper, or other factors. Most lockpickers would probably consider a tip between 1 and 5 per box acceptable—but again, it varies.
If you have only one or two lockboxes, put them in the "Will not be traded" slot of the trade window. Otherwise, you can trade your boxes to the lockpicker in bulk and they can unlock them from their inventory, then trade them back to you.
Try asking friends and guildmates before asking strangers. You are more likely to get it opened and more likely to get it done for free. You can mail the boxes to them, and they can send them back unlocked (if you do, list the boxes in the message, so they have a note to respond to, and as a reminder of who sent what).
Patch 4.0.1 (2010-10-12): Lockpicking now skills up as you level, you no longer need to practice. Hovering over your [Pick Lock] icon will show the current level of box you can open.
Patch 1.1.0 (2004-11-07): No longer auto-ranks. It must be used to improve.