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 skewb is a very solid and satisfying puzzle to play with.
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 made 2x3x3 cuboid, invented by Tony Fisher.
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.
Holey / Void Megaminx
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.
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.
Missing Link Key Chain
The 1982 official Rubik's Missing Link Key Chain released by Ideal. This puzzle stands 60 mm tall excluding the keychain, and the keychain's plastic attachement loop.
Whip-It (3 layers)
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.