• Octopuses have no bone, shell or hard part except for a parrot-like beak and teeth. Even the biggest of them can pass through the smallest holes (see it here and here).
• The big giant pacific octopuses are large enough to prey on sharks (video).
• They are considered very intelligent and they can solve problems like unscrewing child-proof bottles to get their food. However they are very different than us because their nervous system is not centralized. Thus if you cut one of their arms, it will still move. Presented with food, the severed arm will try to put it where the mouth is supposed to be.
• Supposedly, octopuses can “see” with their skin, as they are color blind but can still match they color with the environment to camouflage. (yeah this part required further investigation)
• Their suction cups are very strong. They can leave hickeys on your skin (if the octopus let go of you and you can see the result. Otherwise you end up like the shark in the previous video). As they have 2000 of them, it requires a great amount of strength to pull an octopus apart from its prey. They can control each sucker individually. For instance they can pass an object from sucker from sucker to put it in their mouth. And they can also taste with them. 
• Octopuses were observed playing. They can be very curious and playful indeed. I love this video where an octopus snatches a guy’s camera and runs away with it (http://www.youtube.com/watch?v=x5DyBkYKqnM)
• Their lifespan is variable from a few months to 10 or 30 years. The giant pacific octopus lives up to 3 years. About the same as a hamster.
• Octopuses epic skills also include : spurting water, ejecting ink, poison, crushing shells with their hard beak, changing color, changing the texture of their skin, growing back a severed arm. And I’ve already posted a video of the mimic octopus, which imitates the appearance and behavior of other creatures.
• When a female is ready to reproduce, it attracts males with a perfume. The male donates its sperm then leaves. Then the female spends a long time looking for an appropriate nest. It lays hundreds of thousands eggs, impregnating each one and weaving them onto big clusters. The female can spend 6 months continually taking care of its eggs and finally dies after they hatch.
• I’ve heard of live octopus sashimi, which are freshly cut octopus arms that still move when you eat them. It’s a very strange experience because the suckers can stick to the inside of your mouth or throat. I’ve just discovered that it is a tradition in Korea to eat whole octopuses alive. As the octopus goes down your throat, it can get stuck and you can choke on it. So it’s like a courage trial to eat them. Here is the video.
  As I developed a fondness for those animals, it’s a bit strange for me to see these videos of octopuses still moving when you cook or eat them. But when you think of it, you cook lobsters or crabs this way. And you also eat oysters alive. So well, it’s just customary. (even if an oyster is not nearly as intelligent…)
• Tree octopuses are a hoax (I didn’t realize at first…)

References :
http://www.orionmagazine.org/index.php/articles/article/6474/
http://www.orionmagazine.org/index.php/newsfrom187/entry/6591/ 
(2 very interesting articles) 
and of course wikipedia, youtube, etc