Although there are already a few reviews on this series, AOT is so good that I still felt the need to write a review.
Attack on Titan is, at the time of this writing, only 8 episodes into the series, yet it already seems to be one of the best anime of 2013. I'm a big fan of SAO and this series is right on par with part 1 of SAO (if you're reading this and Haven't seen Sword Art Online, I would very highly recommend it- definitely one of the best anime I've ever seen.)
**Here's a quick note- if you aren't sure whether or not you'll want to watch this, here are some things that could keep you away. There IS gore in AOT, and while it lessens up later, the first few episodes are particularly gruesome compared to shows like Naruto or One Piece. If you're interested but not big on the gore, try watching Psycho Pass. It's a great anime in its own right but it's also not afraid of some blood. If that show has too much Gore for you then you probably won't like AOT. Also, if you get scared easily, these Titans are extremely creepy. Like, Evil-Clown level creepy. In the end, wouldn't recommend for early teens.**
Some reviews have given confusing accounts of what Attack on Titan is about (I'm looking at you blackmamba99971) whereas others have given much more concise sums (fanis-gav has a good one) but basically, it's a Medieval-looking time period and humanity lives in the spaces between 3 separate circular walls (Great Wall of China sized walls) one inside of the next. These walls were put up to protect humanity from the Titans, humanoids with no "junk" that go in sizes of 5, 7, 15, and 60 meters (A tall human is 2 meters by the way). No-one knows where the titans came from or how they survive/reproduce or even how they can be killed for awhile. All they know is that Titans eat humans simply because they enjoy it. After "100 years of peace" living within the walls, the Titans break through a part of the Outermost wall where a young boy named Eren lives. To put it shortly, he sees some people killed right in front of him and vows to "wipe out each and every Titan."
Now here is where the show really sets itself apart. In most anime, the main character has some secret power or something that allows them to live up to their challenge. Naruto had a ton of chakra, Luffy had the Gum-Gum fruit and Ichigo had an intense Spiritual Pressure. All these MC's have something exceptional about them that makes anything seem possible.
This is anything but the case for Eren. When we meet Eren, he's a scrawny little punk that can't even take on others his age, much less an adult or Titan. The idea of Eren taking on a few of the lower level Titans is laughable. Even after a 5 year time-skip where Eren and other kids have become young adults trained to kill Titans with the Recon squad (a unit of the Army that goes outside the walls to fight Titans and has little to no success at this point), they look like as big a threat to Titans as a toddler with a wooden gun. And you see it in every episode too; the feeling that no-one is safe and the desperate plight that the characters are in really permeates the entire show. There's no "Last-Second-Save" like in most other anime, and the twists come every week. You get to know a whole cast of characters but you never know who's safe or not. This adds a gravity, a realness to the show that brings you in and really allows you to connect with these all too fragile, human characters.
Besides that, the artwork is fantastic, the soundtrack gets better each episode, the character and plot development is top-notch and there's still a ton of room to grow with where the Titans come from, what Eren's dad injected him with (we still don't know), what's in the basement and how the Colossal Titan keeps appearing. If you can deal with a bit of gore and are looking for a great new show, it's a fantastic piece of work well worth the look.