Kasumi - Stolen Memory
Kasumi - Stolen Memory adds an additional character for you to recruit on your mission. Kasumi Goto is a master thief, who can steal anything without being detected. As with the other squad members on your team, Kasumi has her own loyalty mission for Shepard to complete, as well a new type of SMG for you to pick up.
Kasumi's loyalty mission is a very interesting diversion from the other kinds of missions, and having another character in your stable is very handy. Kasumi has some really cool and powerful abilities, so I'd say this one is worth checking out.
Overlord
The first main story mission DLC, Overlord has you investigating another Cerberus project where the shit has hit the fan. A VI has gone rogue and it's up to Shepard to figure it all out. After fighting your way through Geth enemies, you find out the horrifying truth behind the project.
The Overlord mission is decent, and it is a decent length. I would say though that out of the DLC packs, it's not essential to play through. If you really enjoyed playing ME 2 like I did though, it's definitely worth grabbing.
Lair of the Shadow Broker
The elusive Shadow Broker has been around seemingly forever. No one has ever seen the Shadow Broker and no one knows where he is. He wields enormous power, able to get seemingly any information. As you may remember, Liara T'Soni (squad member from the first Mass Effect and possible love interest) played a relatively minor role in Mass Effect 2 proper, giving you a mission or two, working as an information dealer herself on a crusade to find the Shadow Broker to repay a debt. Liara contacts Shepard, having come into possession of information that might shed some light on the elusive information dealer.
Lair of the Shadow Broker is definitely the best DLC for ME 2. Everyone who owns the game should get it. In the regular game, Liara is not very well fleshed out, and frankly a shell of a character. It was almost painful how little use she had. This DLC completely fixes this oversight and more. Assisting Liara on her crusade against the Shadow Broker is the most satisfying mission in the entire game, without a doubt in my mind. Plus, it helps create some much needed continuity between the first game and ME 2. If you have Mass Effect 2, buy this. The only knock I have against it is that it is more expensive than the rest of the DLC, at 800 MS/Bioware points.
Arrival
The final Mass Effect 2 DLC pack, Arrival sets the stage for Mass Effect 3. Admiral Hackett calls in a favor to have Shepard check out a friend that has been arrested in Batarian space. Dr. Kenson was on a deep cover mission to investigate rumors of a Reaper artifact in the Batarian controlled sector that supposedly has evidence of the impending Reaper invasion. She was arrested on terrorism charges. Hackett wants you to free Dr. Kenson and investigate the invasion claims.
Arrival is notable for setting up Mass Effect 3, but the actual mission itself could be better. For the most part you're just doing the usual combat, though there are achievements for using stealth and what not. For a Mass Effect fanboy, it's worth the price, but similar to Overlord it's not essential.