I've been building and buying Rubik's cubes since I bought my first cube in 2009 or so. Here is my collection so far:
Rubik's Revenge (ITC)
Follow up to the Rubik's cube, as shown by its name.
Produced in 1982 and 1983 by Ideal Toy Corporation in Korea, Macau and Hong Kong.
6X6X6 & UP
The first mass produced 6x6x6. A six layered cube.
The first 7x7x7. A seven layered cube.
CUBE (SHAPE PRESERVING)
A twisty puzzle cube that turns around its corners. It has five layers per throughgoing axes.
An incredible creation by Katsuhiko Okamoto. A very rare puzzle for many years it became mass produced in 2011.
A corner turning hexahedron. Very similar to the MasterSkewb but without its corners.
The deepcut corner turning cube.
CUBE (SHAPE CHANGING)
A Rubik's Cube with edges that turn by gears.
Fisher's Golden Cube
All the stickers on this 78 mm modified Skewb are the same reflective golden colour. There is only one solution.
A 3-D puzzle solely based on gears.
Micro Axis Cube
A very popular shape transformation of the 3x3x3 dramatically reduced in size.
A puzzle which reminds one of the Square-1 but introduces a whole set of changes to the original set.
2x2x3 (aka Slim Tower)
A formerly custom now mass produced 2x2x3 cuboid, commonly known as the "Slim Tower"
Custom 2x3x3 cuboid, made from a 3x3x3.
The long awaited bigger brother of the 2x3x4.
A fully functional and fully proportional 4x4x6 made from a 4x4x4.
Curvy Octahedral Megaminx
A megaminx in octahedral shape. It is not a shape transformation but designed from scratch.
Meffert's build-up and truncation of a Skewb into an octahedron.
A 3x3x3 equivalent to the fused cube. It was radically truncated.
The Holey Megaminx or Void Megaminx - inspired by the Void Cube this is a megaminx without centres.
Meffert's version from 1982 with six colours.
Essentially a Deeper cut megaminx at heart, the Pyraminx crystal adds a new twist to the classic puzzle.
Pyraminx (Tomy 1981)
The 1981 Tomy version. Most samples came with logo on the yellow face.
A Bump Cube (aka Mirrorblocks) truncated into a cuboctahedron.
DaYan Gem I
An edge turning hexahedron transformed into the shape of a truncated octahedron which is an archimedean solid.
The first puzzle in a series of Truncated Kleetopes -- this version is a Truncated Triakis Tetrahedron.
A 2x3x3 truncated into a random assymmetrical shape.
A Platypus dyed and stickered to change the look into that of a classic puzzle.
Whip-It 3x6 (cylindrical)
This 3x6 Whip-It stands approximately 7 mm tall. Produced in Macau. Original LJN Whip-Its were made in Hong Kong.
SIAMESE & FUSED
Cubie Chaos 1
A small number of Eastsheen 2x2x2s joined and extended to form a 2x4x5 block which poses a new kind of challenge.