This is my current collection of owned twisty puzzles. I can solve each of them.
The first mass produced bandaged 3x3x3 with only one unbandaged piece.
Toys Tiled Cube
This plain tiled cube suffers from the same lack of quality common to all the "Toys" cubes.
A 3x3x3 with a hole through the center.
This 50 mm white plastic cube has painted dots instead of stickers.
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.
Taking the concept of the Rubik's cube and turning it 45 degrees.
A 3x3x3 variation built by Katsuhiko Okamoto.
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.
Of this 3x3x3-variant only few examples were produced and sold in the eighties.
This is a newer version of the Megaminx, published by Meffert, with tiles and 12 distinct colors.
A higher-order Pyramorphix. A 3x3x3 transformed into the shape of a tetrahedron.
SIAMESE & FUSED