Here are puzzles I would like to own but do not. They range from way too expensive, to possibly obtainable.

From Fiddl'Widdit Wire Puzzles:	Bridge (copper)	Star Maze	Heartful Dodger	Double Heart Loop
	Ring Trapper	Triple Trapeze	Ski Doodle	Triamese Angels
From Family Games, some tanglements from their IQ Collection. You might be able to find them at these resellers: ToysGamesPuzzles Puzzlesusa.com Educational Learning Games	Sproing	Mental Maneuver
From Livewire:	Paper Clip
From Uncle's Puzzles - Cuffed. Seen at Seriouspuzzles.com.

Toe-Key-Yo

Hel-Sin-Key

Beer Stein

Some new twisty puzzles available from The TwistyPuzzles.com Shop: Turbo Mind Twister, Ball.B with orange dots, Ball.B with flags		Coming soon from Gentosha, the 2x2x3:
The Path - from Family Games	From Puzzlemaster.ca, new trick locks by Rainer Popp:
Hoodoo Loop	Crazy Campers	Regatta
Zookeepers Nightmare - Smartgames	Slocum and Botermans have a new puzzle book out - so far, only in the Netherlands - Het Ultieme Puzzelboek	AreYouGame has Knight's Move
Temple Games produces Brain Art Level 4, Infinity, and Triangular. (links to cardhaus.com)	Game Birds by Pentaplex
The Pattern Box by Kagen Schaefer	Ivan Cube - by Leonid Mochalov - available from Puzzlewood.de	TanCube - available from Puzzlewood.de

Over the years, there have been many variations on the Rubik's Cube type puzzle where elements held within the puzzle can be rearranged. There are also custom versions made by enthusiasts, some of which (both the person and the item) have become well-known in the puzzle collecting community. The table below shows some of the items I will add to my collection as serendipity permits.

Key:

Tetrahedral Puzzles
Hoberman BrainTwist	Pyramorphix
Mastermorphix (traditional)	Mastermorphix (truncated)	Mastermorphix (pillowed)	Reuleaux Mastermorphix	Mastermorphix (Mefferts)
Megamorphix	Curvy Megamorphix	Ultramorphix
Pyraminx	Tetraminx	Mastermorphynx	Master Pyraminx	Reuleaux Master Pyraminx (Cowan)
Halpern-Meier Tetrahedron	Edges-only HM	Reuleaux Halpern-Meier Tetrahedron (Cowan)
Master HM Tetrahedron (Cormier)	RX	Elite Tetra. (Cormier)	Royal Tetra. (Cormier)
Greenhill's Square-1 Tetrahedron	Danger Cube
Cubic Puzzles
Rubik's Pocket Cube, Rubik's Cube, Rubik's Revenge, Professor Cube		V-Cube 6x6x6, V-Cube 7x7x7	Mefferts Bandaged Cube
Other Cube Makers Rubik's Studio Cube, Politoys Cube, Eastsheen A4, Eastsheen A5
Skewb	Master Skewb	Elite Skewb	Dino Cube (2 color), Dino Cube (4 color), Dino Cube (6 color), Dino Cube (Dinos)
Rex Cube	Praxis Cube	Lattice Cube	Shallow Dino	Rhino
Cowan's Super-X
24 Cube (Shepit)	Helicopter Cube	Hexaminx (Pillowed) (Traiphum)		Square-1, Super Square-1
Fisher Cube	4x4x4 Fisher Cube	Windmill Cube	Greenhill's Cube	Alokin's Slice Cube
Axis Cube	Ghost Cube	Cubic 3x3x5	Golden Cube	Cubominx
Kite Cube	Aleh's Brilicube	Babyface	Einstein Cube
Edges-only Cube	Edges-only 4x4x4	Bump Cube Junior	Bump Cube (Mirror Blocks)	Void Cube
Cubic Sticker and Shape Variations, Heads
Rubik's Cube 4th Dimension	Ultimate Cube	Rubenking	Calendar Cube, Kalendar Kubus	8-color Cube
3-color Cube	Fused Cube	Ball-in-Cube, Cube-in-Ball	Truncated Cube	Half-Truncated Cube
Friki (2x2x2 Cuboctahedron)	3x3x3 Cuboctahedron	Master Cuboctahedron	5x5x5 Cuboctahedron
Mama Skewb	Rainbow Cube
Diamond Cube	Rhombi-Cuboctahedron	Hexagon Rhombic Dodecahedron	3x3x3 Octagonal Prism	Pillow Cube
Confused Pillow Cube	Chicken Cube	Original Toys Cushion Cube	Original Toys Rhombic Dodecahedron	Socube Rhinocerous
Morph	Bart Simpson, Homer Simpson	Darth Maul Kellogg's set of 6 2-sided Star Wars Heads	Set of 9 Warner Cartoon Heads
Cuboids, Extended Cubes, Evil Twin/Chaos, Siamese
1x1x1, 1x1x2, 1x1x3, 1x2x2, 1x2x3, 1x2xN (Telescope), 1x3x3 (Floppy), 1x3x3 (Super Floppy), 1x4x4 2x2x3 (Slim Tower), 2x2x4, 2x3x3 (Domino), 2x3x4, 2x4x4 3x3x4, 3x3x5, 3x3xN (Telescope), 3x4x4, 3x4x5, 3x5x5 4x4x5
Floppy Cube	Domino (groove), Domino (spindle), Domino (Russian), Domino for the Blind, Domino clone	Fisher's Mental Block
Octahedral Puzzles
Okki (Mefferts)	Lolo's Octaeder	Skewb Diamond (Mefferts)	Face-turning Octahedron
Magic Octahedron	Christoph's Magic Jewel	Master Octahedron (Bedard)
Trajber's Octahedron	Master Trajber's	Professor Trajber's	Truncated Trajber's	Edges-only Trajber's
Dino Octa	Rainbow Octahedron	Octaminx
Dodecahedral, Rhombic Dodecahedral, and Icosahedral Puzzles
Pentultimate	Skewb Ultimate
Starminx	Pyraminx Crystal	Supernova (re-issue)	Original Hungarian Supernova (Pentangle)	Megaminx
Ball.B (Ballminx)	Alexander's Star (Great Dodeca.)	Holey Megaminx	Impossible Dodeca., Kilominx	Impossiball
Gigaminx	Teraminx	Petaminx		Dodeca (Nona)
Mobius	Twitchit	Romanian Dodecahedron	Tantrix The Rock	Hungarian Rock
Rua	Toru	Rhombiminx	Dino-Rhombic Dodecahedron (DRD) (Cormier)
Fisher's Icosahedron Skewb	Original Dogic	Mefferts Dogic - I (12 color), II (10 color), VI (20 color) Not shown: III (5 color), IV (2 color), V (2 color)	Icosaminx	Tutt's Icosahedron
Spheres, Ovoids, Pucks, and UFOs
Rubik's Cheese	Kep Korong	Brainbow	3-layer Puck	Tonne
3x3x3 Sphere	Mozaika (8 color)	Cosmos	Bolaris	Quarks
Chromosix	Chromosix Numbers	D-Ball (Globe)	Dreamball (Venus)	Equator
Hungarian Globe	K-Ball (white), K-Ball (yellow), K-Ball (Braille)	K-Ball Swirls, small	K-O Labyrinth	Logi-VIP
Masterball: Rainbow, Duo B&W, Dragon, Circus, Soccer ( There are many variations.)		Skewb-cut Balls (various mechanisms) Mefferts Creative Ball (black), Mefferts Creative Ball (white), Beach Ball, Mickey's Challenge, Skewb Globe		Massage Ball, Massage Ball for the Blind
Rubik's World (black), Rubik's World (blue)	Thomasball (12 rings), Thomasball (soccer) (Other versions exist.)	Wisdom Ball, var., Wisdom Ball Jr.	Mefferts Morph-Egg	Mefferts Skewb Egg
Rubik's UFO (gray), Rubik's UFO (green)
Other Puzzles
4D8	Arancia	Trick Haus	Dino Star	Rhombic Triacontahedron
Astrolabacus	Smart Alex (Black), Smart Alex (White), Alpa-2-Go	Rubik's Rabbits	Tsukuda's Square, Tsukuda's Square (red)	Tricky Disky
Jackpot, NGP	Rotos	Octagon Slider (?)	Rubik's Clock, Compass	GloBall
Jugo Flower	Cohan Circle	Combo	Triple Disky

Stewart Coffin - Triangular Prism

Hesperides

Dalloz 184

From Davan's, a Maruca: 

a Lateral Thinking: 

From Funagain.com,

Criss Cross  

a 35-ball Pyramystery

Here are the relatively expensive items:

FromGarE Maxton:

A set of Hoffman's puzzle repros from John Berkeley