The brain of the octopus is wrapped around its esophagus..."it also shares key features such as folded lobes, a hallmark of complexity, and distinct visual and tactile memory centers" (See below).
I remember reading at one point about the octopus being one of the few animals that may look into a mirror and know it is looking at itself...
"Previous researchers tested octopuses in artificial mazes; Mather and Anderson found ways to observe learning and cognition in more natural circumstances. They charted the efficiency and flexibility with which giant Pacific octopuses switch strategies to open different shellfish—smashing thin mussels, prying open clams, drilling tougher-shelled clams with their rasplike radulae. When served clams sealed with steel wire, for example, octopuses deftly switched from prying to drilling.
Tool use was once commonly invoked as uniquely human. Scientists know better now, but they still cite it as evidence of distinguishing intelligence in chimpanzees, elephants, and crows. Mather describes several ways octopuses use their water jets as tools: to clean their dens, push away rocks and other debris, and drive off pesky scavenger fish.
In 1999 she and Anderson published an even more sensational claim: that octopuses engage in play, the deliberate, repeated, outwardly useless activity through which smarter animals explore their world and refine their skills. Amateur aquarists were the first to suspect that octopuses played. While still in high school, James Wood, now a marine biologist at the University of Texas's marine lab in Galveston, watched his pet octopus grab, submerge, and release her tank's floating hydrometer as if she were a toddler with a bath toy. She also spread her mantle and "bubble surfed" the tank's aerator jets.
Anderson tested for play by presenting eight giant Pacific octopuses with floating pill bottles in varying colors and textures twice a day for five days. Six octopuses examined the bottles and lost interest, but two blew them repeatedly into their tanks' jets. One propelled a bottle at an angle so it circled the tank; the other shot it so it rebounded quickly—and on three occasions shot it back at least 20 times, as if it were bouncing a ball."
Please see Discover Magazine's 2003 article on the Octopus