Is it the 5x5x5 (Prof cube)..look at the innards & mechanism
OR is it the Dogic, has many parts but I found it quite easy to reassemble after accidentally popping all the pieces out (hmm...1st piece was accidental, so my fingers got itchy and I popped all the pieces out eventually..LoL)
OR is it the Megaminx? Any others that I missed?

im gonna say 5x5... yes, it seems simple, but the way that he knew where certain curves have to be is amazing. The dogic isnt really as complicated as a 5x5, i have a broken one sitting on my desk (no, i didnt do it this time! ) Megaminx is a 3x3 mechanism that had the pieces slightly reshaped, and a whole lot more axles added

I would like to nominate the Masterball. Although I have yet to crack mine open to see for myself, its mechanism has been accumulating a fair amount of praise on this board during the past month.

Sandy

The most complicated puzzle mechanism I've conceived of is a 7x7x7 mechanism. If someone ever lent me the use of one of those 3D prototyping machines, the 7x7x7 would be what I'd want to build most!

Even more complicated than that would be the 24 piece cube which can be rotated 180 degrees along each of the 6 "diagonal" planes (the intersection includes two edges and two face diagonals). I can't think of a mechanism which is remotely practical.

if by 24 piece cube you mean a cross of the dino cube and the 2x2, i have a simple mech that i'd like to make

I forgot to mention this intricate little puzzle, it is kinda cool with all the curves and orange peel-shaped pieces within it
But speedcubing with one is really not the nicest experience that I have had

No, I'm thinking of something different. First, imagine splitting a cube into 6 pyramids. Then split each of those pyramids into 4 tetrahedral pieces.

That's the way this puzzle would look. It looks superficially like a Dino Cube, but closer inspection reveals that each "Dino Cube piece" is additionally split along the cube edges.

While it looks like this puzzle could rotate 120 degrees around a corner like a Dino Cube, it cannot (this is hard to visualize). The only possible rotation type is a 180 degree half plane rotation along opposite face diagonals.

I've come up with 2 mechanisms, neither of which is plausibly practical (they require extremely thin "trunks" travelling in myriad lipped grooves on a spherical inner core). The more practical of the two features 12 trunks--one for each edge--each made out of two halves (one of the 24 trunk halves is permanently attached to the core, with many of the grooves only half width). But there are just so many grooves running in so many intersecting and tangential paths, that they need to be outrageously thin compared to the puzzle's size.