Fairly new to twisty puzzles. Trying to grow my understanding and my collection.

3X3X3

Xiaomi Giiker Super Cube
A smart cube with bluetooth connection which allows a separate app to show the owner how to turn the cube in order to solve it.
4X4X4

Crazy 4x4x4 III
The third 4x4x4 with circles on all six sides. The circles are larger as in the first two variants.
CUBE (SHAPE PRESERVING)

4x4x4 Mixup Plus Cube
A mass produced Mixup Cube. Compared with the "3x3x3"-variant three rings are further split up.
Crazy Unicorn
The Unicorn in a crazy version, with circles on the faces.
Dual 3x3x3
Two 3x3x3s in one puzzle with some sides of both parts connected. Five different versions were produced.
Pentacle Cube
A mass produced cube with pentagrammically cut circles on all six side.
Redi Cube
A twisty puzzle cube that turns around its corners. A faceless Compy Cube.
Skewb
The deepcut corner turning cube.
CUBE (SHAPE CHANGING)

Bump Cube
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.
Circus Skewb
A Fisher Skewb with pieces swapped to look like a twister cube.
Fisher Cube
Taking the concept of the Rubik's cube and turning it 45 degrees.
Ghost Cube
A 3x3x3 placed in midturn and reoriented in its original shape. Every piece is of unique shape and therefore sticker can be unicoloured.
Junior Bump Cube
A 2x2x2 was "bumped" to make it look like a Mirror Blocks aka Bump Cube.
CUBOID

3x3x4 (cube4You)
Not the first fully functional 3x3x4 but the first mass produced.
Super 3x3x5 I Cuboid Cube
A 3x3x6 with one layer reduced to a circle, unlinked to the surrounding pieces and with the core shifted by half a cubie.
OCTAHEDRON

DODECAHEDRON

Megaminx 2x2x2
A mass produced Kilominx with straight edges on the pieces but with exposed centers.
Rediminx
A mass produced Dino dodecahedron with spherical cuts.
FOUR

Mastermorphix
A higher-order Pyramorphix. A 3x3x3 transformed into the shape of a tetrahedron.
Megamorphix
An even higher-order Pyramorphix. This time a 4x4x4 was transformed into tetrahedral shape.
THIRTY

Dayan Gem VI
A relative of the Wheel-of-Wisdom in shape of an Alternate Truncated triakis octahedron.
OTHER N-SIDED

Tuttminx
The puzzle is an extension of the Megaminx to a truncated icosahedron (soccerball or buckyball for the chemists).

All 32 sides are rotatable.
SPHERE

Gear Ball
A mass produced spherical Gear Cube.
CYLINDER

STAR

OTHER SHAPES

30-Axis Wisdom Wheel
A variant of the Clover Cube with more pieces per turn and six additional turns corresponding to the face turns of a cube.
Crazy Comet
A jumbling twisty puzzle based on the geometry of a Rhombic Dodecahedron.
Rainbow Nautilus
A dihedral puzzle with fascinating shape, colors and a strange arrangement of cuts.