Traditional block construction toys are dominated by the classic Lego, however the Lord of the Rings movie triggered various construction toys.
There is a specific blog dedicated to Tolkien construction toys called Tolkienbricks, however this covers more than just commercial products.
Intelliblox (Playmates)
This is a small series based on the Fellowship movie. The figures included are actually more like toy soldiers.
Mines of Moria (includes Frodo, Gimli, Moria Orc and Gandalf figures)
Isengard Caverns (includes Uruk-Hai, Saruman and Gandalf figures)
Encounter at Prancing Pony Inn (includes Frodo, Strong Der and Pippin figures)
Battle at Weathertop (includes Sam and Aragorn figures)
Buckleberry Ferry Escape (includes Ringwraith on Horse and Frodo figures)
Orc Attack at Amon Hen (includes Boromir and Lurtz figures)
Mini Mates
Mini mates is not a full construction system, it is only figures however they are based on the style.
Figurerealm has details of those.
There are also some specific sites which have details about these figures.
Series 1
Legolas and Gimli, Gandalf the White and Theodon, Frodo and Uruk-Hai Swordsman, Saruman and Wormtongue, Aragorn and Uruk-Hai Berserker
Series 2
Twilight Frodo and Amon Hen Frodo, Gollum and Sam, Boromir and Merry, Pippin and Uruk-Hai Crossbowman, Grishnakh and Orc Scout
Boxed Sets
These contain 3 characters and 1 hidden character.
Aragorn, Saruman and Legolas
Specials
Elven Archer and Elven Swordsman
Planned (never released)
Series 3
Ringwraith 1 & Ringwraith 2, Eowyn & Morgul Lord Witch King, Lurtz & Twilight Witch King, Strider & Clear Twilight Witch King
Lego
Tolkien Lego is quite extensive and goes further than just the original construction toys, in fact it is really a theme (although I will detail everything here).
Construction Sets
These are based on the Lord of the Rings and Hobbit movies.
The Brickset site has some great details on these sets (and I have given the links where appropriate).
Lord of the Rings movie
Gandalf Arrives (9469)
The Council of Elrond (79006)
Battle at the Black Gate (79007)
Pirate Ship Ambush (79008)
Tower of Orthanc (10237)
Promo
Frodo with cooking corner (30210), Urak-Hai with ballista (30211), Elrond (5000202)
Shop Displays
German
Hobbit movie
Riddles for the Ring (79000)
Escape from Mirkwood Spiders (79001)
Attack of the Wargs (79002)
An Unexpected Gathering (79003)
Barrel Escape (79004)
The Goblin King Battle (79010)
Dol Guldur Ambush (79011)
Mirkwood Elf Army (79012)
Lake-town Chase (79013)
Dol Guldur Battle (79014)
Witch-King Battle (79015)
Attack on Lake-town (79016)
The Battle of Five Armies (79017)
The Lonely Mountain (79018)
Promo
Mirkwood Elf Guard (30212), Gandalf at Dol Guldur (30213), Legolas Greenleaf (30215), Lake-town Guard (30216), Good Morning Bilbo Baggins (5002130), Mirkwood Elf Archer
Comic Con (Micro-scale Bagend)
Press Kit
Promo figures (with Blu Ray movies)
Keyrings
Lord of the Rings movie
Gandalf the Grey, Frodo Baggins, Gimli, Mordor Orc
Hobbit movie
Bilbo Baggins
Magnets
Frodo, Gandalf and Ringwraith
The following 2 were sold separately and together as a pair
Bilbo Baggins
Developer Blocks
These were given to the developers of the Computer Games
They were never on sale to consumers
Summer 2012 Catalogue
US
Minifigures catalogue (unofficial)
Blocks (official Lego magazine)
Board Games
Lord of the Rings (Battle of Helms Deep), Hobbit (Unexpected Journey)
Computer Games
Dimensions
This is really a computer games system.
Starter Set with Gandalf figure (versions - PC, PS3, PS4, XBOX 360, XBOX ONE, WII U)
Lord of the Rings movie
Hobbit movie
Draw string bag (promo)
T-shirt (promo)
Posters
Limited Edition 15000
Comic-Con Promo
2013 Calendar
Fake Lego
The following are various fake lego items.
Lele
79001
Hobpit (Hobbit)
Sheng Yuan
SY251
SY206
Lepin