Mathematical toys? Anybody know of "serious" mathematical ornaments or toys like the Gömböc,
etc?
Already have a rubix and abacus (that's more of a tool though).
 A: The Rubik cube. ${}{}{}{}{}{}{}$
A: Spirograph from Hasbro. You can make lots of famous mathematical curves with its pieces: epicycloids, hypocycloids, etc. MathWorld has an article on some of these curves.
A: Zometool is a construction kit which has 2-, 3-, and 5-fold symmetry, which is great for building (3D projections of) the 120-cell, or just for playing around.
A: Wikipedia has a section on mechanical puzzle.
As for myself, my fascination with algebraic topology began with metal link puzzles or hanayama. 
Of course, Tower of Hanoi is a classic.
Of interest may be the reference: Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine, and Other Mathematical Toys by David Joyner. Book description in Amazon.
A: While it may be a 'children's toy', the Switch Pitch works remarkably well as an object of mathematical sculpture; it's fundamentally based on the fact that the vertices of a regular cube are also the vertices of two (interlocked) regular tetrahedra (if your cube is $\{0,1\}^3$, take the vertices with $i+j+k$ respectively odd or even).  It helps that people can't help but fiddle with it; it's been a perfect hand-fidgetting toy for me.
A: The Oloid is fun to touch, to watch and understand. 
A: Maybe a Tippe Top.
A: Love zometool [1]
[1]: http://www.zometool.com/  for geometry, platonic and archimedean solids, among others/
A: Double pendulum. 
A: http://tavernpuzzles.stores.yahoo.net/puzzle.html http://ep.yimg.com/ca/I/tavernpuzzles_2188_4561747
Goal: Remove the big ring
http://tavernpuzzles.stores.yahoo.net/puzzle.html
A: For when the Möbius strip is too pedestrian, the good people at Acme Co. claim their Klein bottles are the "finest closed, non-orientable, boundary-free manifolds sold anywhere in our three spatial dimensions."
A: On Shapeways, you can find a variety of mathematical ornaments.
My favorites are the differential geometric surfaces designed by Bachman.  I also like Bathsheba's designs as well.

(Sorry the image is so large.  Is there a way to reduce the size?)
A: I have a Rattleback at my desk.  Fun to fiddle with while thinking.
A: I think there are 2 different toy devices that mimic a Gray code.
One can be seen at http://mypuzzlecollection.blogspot.com/2011/12/brain.html.
The other is named "Spin Out".
A: Check Montessori mathematical materials like the binomial cube just google it
A: Sudoku and all other logic trainers would also fit.
A: Origami to fold shapes to find surface area of 3 dimensional shapes.  Wooden blocks.  The Game of 24.  Math Jeopardy.  Bucky balls.  Sudoku.  Computer games with rotations and other types of transformations.
A: In a blatant reference to my own creative work, I submit for your consideration the mathematical artwork presented on my Shapeways Shop at this address: https://www.shapeways.com/shops/Feingold_Math_Art
But there are a huge number of other artists whose work can also be found in other shops there.
