Not only music, movies, drawing and photography are part of my hobbies.
For quite a while are so called "magic cubes" also one of my hobbies,
thanks to my collecting tick.
My collection is not restricted to only cubes so calling it "puzzles"
or "brain teasers" would fit better.

That'S my little collection (old state, there are some more right now).

the known "Rubik's Cube", "magic cube" or for cubers "3x3x3"
The left one has stickers (stickered) and the right one
has colored plastic pieces (tiled).
There are countless algorithms to solve it and depending on the method
you need to memorize different ones.
Of course, it's possible to solve it with logic, but very much people are able to do that.

"3x3x3 speedcube", DIY (do it yourself, delivered in parts)
By the popularity of the famous "Rubik's Cube"
of course there are also imitations and improved versions, which are
made of lighter parts and with springs inside and lubing for faster movements.

Nowadays it has become a sport to solve cubes,
which is called "speedcubing"
Since many years there are several "speedcubing" competitions,
in which the best cubuers compete against each other.
They also use other cubes than the Rubik'S Cube (see below) but first of all
it's about the time the "speedcuber" need to solve it.
The current world record was set by Mats Valk
with a time of 5,55 seconds (2013).

My current personal best is about 45 seconds.
(with the Dayan Zhanchi speedcube)

"3x3x3 Void Cube", the holy Rubik'S Cube
Because the "Void Cube" is missing the axes in the middle,
it has a complete different mechanism,
but can be solved like the normal 3x3x3.
However it has a parity error
(switched sides / middle pieces) because of the missing axes
where the side can be misplaced three-dimensional.
The same parity error can be created by removing the stickers
of the middle pieces of a normal 3x3x3.
But the Void Cube is way cooler. ;P

"3x3x3 Number Cube"
This one has a higher difficulty because all 6 sides have the same numbers
and because each number could be also on a different side
or being switched with each other this cube also has a parity error.
The even harder version is the "Sudoku Cube" where you don't really know
which number from 1-9 is on which side.

"3x3x3 Mirror Block" or "Silver Bump Cube"
Solved like a 3x3x3 but obviously there are no colors or numbers
which need to be arranged but the pieces to form the original cube.

"3x3x5 Extended" in silver
This puzzle also exists with colored stickers but the silver version
has to be also arranged to get its original form.
"Extended" means there are layers glued together
so not every layer can be turned, which means it can be solved like a 3x3x3.

"Floppy Cube" or "3x3x1"
Not much to say about it because there's no real algorithm to solve it.
Actually it's so easy everyone can do it.

"4x4x4" or "Rubik's Revenge" or "Rubik's Master Cube"
It is solvable with 3x3x3 algorithms but has parity errors in the end
which can be corrected with two more algorithms.

"5x5x5" or "Rubik's Professor's Cube", also available as V-Cube 5
can be also solved with 3x3x3 algorithms
and with the additional two from the 4x4x4 to correct parity errors.

"V-Cube 6" or "6x6x6"
Same algorithms can be used as for 4x4x4 or 5x5x5.

"V-Cube 7" or "7x7x7"
Also the same algorithms can be used.
It's one of my favorite cubes and I solve it in about 30 minutes.

"Pyraminx"
On this one there's only a small algorithm more specifically just a trick
you need to know to solve it which makes it pretty easy.

"Megaminx" or "Dodecahedron"
Many tutorials explain how to solve it with the 3x3x3 method
but actually it's just putting together edges and for the last layer
you need a few algorithms which can be hard to learn for newbies
because it's an untypical form and sometimes you don't know where is left or right.
The sequels are Gigaminx, Teraminx and Petaminx.

"Super Square-1"
This is the big brother of the "Square-1".
At the moment this is the hardest cube (for me) of all puzzles I own
because the method to solve it is completely different and
not only the colors are mixed but also the shape is deformed.

"Rubik's Snake" or "Rubik's Twist"
This is a snake where every piece can be turned.
If you know how it's not really a challenge anymore.
The actual solution is this ball
but there are many other shapes to build.

"Snake Cube"
At first sight it looks like a 3x3x3 with checkerboard pattern
but disassembled it forms a kind of a snake.
Compared to the "Rubik's Snake" it doesn't form a straight snake form
because obviously you wouldn't be able to build a cube with it.

"15-Puzzle"
Almost everyone knows this small sliding puzzle because it often
could be found in magazines for children but in this case with pictures on it.
Not all of these have a backside because some are in a case and not like this one in a frame.
I still haven't figured out how this pattern on the back is meant
to be put together even after years.

"Varikon Tower"
This variation of the "Babylon Tower" is easier to solve because
this one has only 4+1 layers and the colors don't go from bright to dark.

more to come...

already in collection (but without pictures or info yet):
Square-1
Skewb or Pyraminx Cube
3x3x3 Mini
3x3x3 Star
Super Floppy Cube or Scramble Cube or Super 3x3x1
Domino Cube or 3x3x2
Gear Cube or Caution Cube
Edges Only Void Cube
Fisher Cube
Rubik's Magic
Rubik's Master Magic
Brainball
Siamese Bump Cube
Cake Cube
Diamond Cube
Tower Cube or 2x2x3
Magic Rainbow Ball