This started out as an exercise in making the smallest ball joint tentacle that I could get to print reliably on my printer. It turned into a cute little octopus when I decided to make a fun gift out of the tentacles. It's surprisingly annoying and time-consuming to build, since each segment needs to be hand-trimmed of support and carefully snapped into the next, but the resulting toy has a lot of flexibility and posability.
Printing the segments in all different colors to make a rainbow octopus is optional but highly recommended.
Update 4/5 - I was experimenting with some freehand sculpting tools, and created a big-eyed alien head for the octopus that I've uploaded.
Update 4/7 - added a fantasy steampunk submarine version of the main body.
Update 4/9 - skull body remixed from http://www.thingiverse.com/thing:4126
Print one body piece, one of the x8 tentacle end prints, and 7 or so of the x8 tentacle segment prints. You can print more or less of the segments depending on how long you want the tentacles to be. The tentacle segments and tentacle ends have support material already added which you will need to trim away after printing. I have also included individual tentacle segment and end pieces with and without support.
The center body is provided in two versions. One with support material, and one clean version without support if you prefer to have your slicer program add support.
I printed the center body at 15% infill, and the tentacle segments at 100% infill for strength and because there's hardly any volume to them anyway.
Carefully press each ball on a tentacle segment or end into a tentacle socket or socket on the central body to make all the tentacles.