Rogues are the premier melee DPS class in the game. They are the only melee class with reliable crowd control and as such can be the most reliable melee DPS in instance and raid situations. Played correctly they can have very high survivability having excellent abilities to reduce/eliminate threat and selectively deal with mobs. They are also unique in that all three of their trees are capable of producing respectable DPS, it is more a matter of how the player wishes to get there.
Strengths: First of all, stealth is one thing that sets the rogue apart from other classes(cat form druids being the exception). The rogue has the ability to choose when combat will occur and put themselves in the best position to succeed. They have very high burst damage, especially when attacking from stealth. They also posess a very powerful, long lasting CC (sap) and abilities to return to stealth once the fight has started. They also have strong "stun-lock" abilities, virtually negating a mob's ability to hit them back.
Weaknesses: Multiple mobs are the biggest weakness. Rogues will have to work hard to control pulls because they have comparatively weak armor and most of their abilities focus on single target DPS. They are the "squishiest" of the melee DPS classes so they must avoid multiple pulls and "wars of attrition".
Strengths: Great damage and CC. They are incredibly useful in instance settings, being able to eliminate one mob per pull till the group is ready for it. Once fighting has started they can put out a high level of burst damage on par with or better than any other melee DPS class.
Weaknesses: none to speak of. Range can be a bit of an issue for certain fights as they have to be in melee range to do damage. Other than that, rogues do two major functions in groups and do both of those extremely well.
Strengths: Stealth and stun-lock. You probably won't see them coming and you may not get a chance to do any return shots once they hit you. Rogues seem almost designed to PvP. Add in their ability to vanish and flee combat if things go against them and you see why they are considered a very strong PvP class.
Weaknesses: Low armor and health are the two biggest ones, however taking advantage of those can be problematic. The other weakness has to do with other players. Most players who have the chance (me included) will mercilessly kill any rogue of any level they can. If another player can see through the rogue's stealth and hit from range, you're in serious trouble.
Assasination: This is mostly a crit heavy spec for the rogue. This spec focuses more on burst damage than the others. a lot of enhancements to "stun-locking" come from the assasination tree.
Combat: This is the toe to toe melee tree. A lot of people see combat (swords) as the most efficient leveling build for rogues. This tree has a good balance between offensive and defensive abilities.
Subtlety: This tree focuses on stealth and abilities around that. It boast an ability to increase a rogue's movement speed in stealth among other improvements.
Personally, rogues just aren't for me. Been there, done that. I can't justify leveling a character just to be able to open locks for free (thats why you level blacksmithing or engineering). However, they do have a number of strong abilities and should not be ruled out for someone looking for specific qualities. If you want to use stealth and sap abilities to manage multiple mob pulls, the rogue is the way to go. If you are someone who like world PvP and enjoys ganking defenseless players, you have lost any amount of respect I have for you, but you may consider the rogue as a means to ruin other players' experiences.