My humble collection
CUBE (SHAPE PRESERVING)
A 2x2x2 with a twist that defies all attempts of classifying.
The skewb is a very solid and satisfying puzzle to play with.
CUBE (SHAPE CHANGING)
The Bump Cube is a simple 3x3x3 Rubik's cube, but with an interesting twist. It spawned a whole series of puzzles and created a verb of its own.
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 midturn 3x3x3 still in hexahedral shape but with such an awkwardly oriented axis system that every piece is uniquely shape and therefore sticker can be unicolored.
A face-turning dodecahedron with a mixture of pieces from other puzzles with this axis system.
This is a newer version of the Megaminx, published by Meffert, with tiles and 12 distinct colors.