Dom has an exclusivity contract with Tama drums. He has had many kits several of which have been destroyed during performances. Here it all is. All drums with chrome hardware unless otherwise stated.
Unknown Period
This section is for drums whose time of life is unknown.
British racing green Starclassic Maple kit
Brown fade Starclassic Maple kit
Marigold sparkle Starclassic Maple kit with chrome hardware
As Seen On: Hullabaloo DVD2
Unidentifiable low-end black Pearl kit (Forum, perhaps)
Early Days
Black Tama Starclassic Performer
Used: Live, As Seen On: Muscle Museum II clip, Fate: mortal wound dealt by Matthew
Red w/ silver stripe on kick DW
Used: Live, As Seen On: Muscle Museum II clip, Fate: guitared in the face by Matthew
Unidentifiable yellow kit
Used: Live, As Seen On: Muscle Museum II clip, Fate: unknown but the smart money says that Matt thoroughly owned it
Brown Peavey kit ( possibly a Peavey Radial Pro 1000 ) with distinctive collars around the tom bearing edges (Peavey logo can be seen in this image: [1])
Used: Live, As Seen On: Muscle Museum II clip, Fate: as above
Black Yamaha Recording Custom kit
Used: Uno clip, As Seen On: Uno clip, Fate: Unknown
Nondescript DW kick drum and 14x5.5 matching snare
Used: Sunburn clip, As Seen On: Sunburn clip, Fate: Unknown
Origin Of Symmetry period
Matte Black Pearl Masters kit and 14x6.5 LB417 Ludwig Black Beauty snare
Used: New Born clip, As Seen On: New Born clip, Fate: Unknown
Silver Sparkle Sparkle Tama Starclassic Maple kit and 14x5.5 matching snare
Used: Live, recording Origin of Symmetry, Plug In Baby, Hyper Music and Feeling Good clips, As Seen On: Plug In Baby, Hyper Music and Feeling Good clips, Fate: Brokeded by Matt and Chris
22x16,12x10,14x14,16x16
White Matte Starclassic Maple Kit with hollographic tama emblem.
Used: As with the silver sparkle tama, the white starclassic was used during the origin of symmetry tour of japan in 2001, Fate: Dismembered by matt and chris during bliss in their final show of the tour.
Blue and Red DW kit and Orange 14x5.5 DW snare
Used: Recording Origin of Symmetry
Blue: 22x18,14x12 Red: 12x8,16x14
Dead Star/In Your World period
Blue Sparkle Tama Starclassic Maple kit and 14x6.5 Ludwig Black Beauty snare (hammered shell, Imperial lugs)
Used: Dead Star and In Your World clips and live, As Seen On: Dead Star and In Your World clips and Hullabaloo DVD1, Fate: demolished by Matt
22x16,12x9,14x14,16x16
Absolution period
Amber, Red, Yellow and Blue Vistalite kit
Used: Stockholm Syndrome USA clip, As Seen On: Stockholm Syndrome USA clip, Fate: Unknown)
12x8,13x9,16x16,22x16
Custom Chrome Tama Starclassic Maple kit with custom black powdercoated hardware and matching 14x6.5 snare
Used: live, As Seen On: Absolution Tour DVD, Fate: Matthewed many times (this kit was reincarnated at least thrice).
22x18,12x8,14x12,16x13
Yamaha Maple Custom Advantage kit and 14x5.5 Yamaha Brass snare
Used: Time Is Running Out Clip, As Seen On: Time Is Running Out clip, Fate: Unknown
Blue DW kit and matching 14x5 snare
Used: sessions for Apocalypse Please, Time Is Running Out, The Small Print, Thoughts of A Dying Athiest, Sing For Absolution and Fury, As Seen On: Absolution Bonus DVD, Fate: Unknown
Composite Kit
Used: recording Apocalypse Please march, As Seen On: Absolution Bonus DVD
22x18 black walnut satin Ayotte, 22x18 blue opal DW
Composite Kit
Used: recording Ruled By Secrecy, As Seen On: Absolution Bonus DVD)
22x18 black walnut satin Ayotte, 12x9 and 16x16 blue sparkle Tama Starclassic Maple toms, 14x5 silver DW snare
Composite Kit
Used: practicing before recording Ruled By Secrecy, As Seen On: Absolution Bonus DVD
22x18 black walnut satin Ayotte, 14x5.5 silver sparkle Tama Starclassic Maple snare
Black Holes and Revelations period
Composite kit
Used: recording the album
Wooden kick, 12x8, 14x12 and 16x14 clear Ludwig Vistalite toms
Crystal Ice (clear acrylic) Tama Starclassic Mirage kit with custom white powdercoated hardware and matching 14x6 snare or 14x6.5 Tama Power Metal Brass snare
Used: live, Supermassive Black Hole and Knights Of Cydonia clips, As Seen On: Supermassive Black Hole and Knights of Cydonia clips
24x18(w/Tama Power Kick Bass Muffler),12x8,14x12,16x14,20x14 Mirage gong bass
Fate: Sold as part of an Auction for Oxfam
Bubinga Tama Starclassic kit (Black Metalic w/ Gold Inlay) with black nickel hardware and Tama Power Metal Brass snare.
Used: Live Williamsberg, supporting My Chemical Romance
Fate: Likely retired, as with above
Vintage Gretsch Jazz Kit in a Champagne Sparkle Finish
Used Wembley Stadium 16th and 17th June - Soldier's Poem, Unintended and Blackout
The Resistance period
Dom now endorses DW drums.
8-ply Maple (possibly VLT), either Gold sparkle with Gold hardware or Silver custom finish with Chrome hardware (he has been spotted using both live) with a 14x6.5 Aluminum DW snare or Ludwig *LB417 Black Beauty of the same size
Used: recording the album, live
22x20, 12x10, 14x14, 16x16, 21x16 Gong bass
Dom uses a Roland TD20kx V-Drums kit for Undisclosed Desires
He also uses two kettle drums live during Exogenesis Pt1
Fate: Active duty
Dom is left handed

As Dom is left handed he sets his drums up with the hi-hats on his right and floor toms on the left. If you're right handed look in a mirror basically.
Cymbals

See Cymbals
Hardware

He uses a Tama Iron Cobra Lever Glide Hi-Hat stand and used to use Iron Cobra Power Glide double and single bass drum pedals interchangeably depending on the setlist (few songs require the double, Cave live, for example) but now uses, with all but total exclusivity, a Chrome Cobra single.
His hardware is Tama Roadpro, his throne is a Tama First Chair with back-rest and he has used Zildjian Dennis Chambers signature series drumsticks, Shaw 5BN drumsticks (Hullabaloo) and Promark TX5BNs (Live 8, and BH&R tour), Marco Minneman signature sticks, as well as many others. Dom also has had his own signature drumstick released through Promark, and it is currently available to the public for sale in the UK, and by special order in the US.
Heads

He uses Remo and Aquarian heads. Dom generally uses the classic combination of clear Emperors over clear Ambassadors on his toms (coated Emperor in the OoS period), but has been seen with Pinstripe batter heads (on the Peavey kit).
The following combinations have been seem:
Silver sparkle: Super Kick II with no resonant side head
Blue sparkle kick: Super Kick II over black ported Regulator
Chrome kick: Powerstroke 3 over black ported resonant side head
Ayotte kick: Powerstroke 3 over unknown resonant side head
Crystal ice kick: Super Kick II over Force I or Powerstroke 3 over unknown clear ported Remo or Pinstripe over ported Pinstripe
Coated Emperor, Controlled Sound or Hi-energy (Hullabaloo only) batters on his snare.
Note the one exception to this rule is when he uses the stock Tama heads, Evans clear G2 over clear G1, that come with every new kit of drums. As the G2/G1 combination is identical to his usual Emperor/Ambassadors he'll often use the stock heads until they wear and replace the batter only.
Contract Lapse

It is possible that during 2005 Doms endorsement contract with Tama Drums expired as a set of orange and red Ludwig Vistalites (acrylic drums) were used in the USA cut of the Stockholm Syndrome video clip (and another character in the talk show was using Pearl drums). As video clips receive much public exposure it is usually against the terms of a contract to use a competitors product. This would tend to suggest that the Tama contract had reached its conclusion.
A clear set of Vistalites (with a shallower rack tom, 12x8 most likely) is seen on one of the background images of Muse's official site, suggesting that they were used for the recording of Black Holes And Revelations.
As of 2006 he is using Tama Drums' new Starclassic Mirage line [2](acrylic drums) in live situations. These three data would suggest that the contract briefly lapsed in 2005 and during that time Dom developed a tatse for acrylic drums. When Tama released Mirage he renewed his endorsement.
Other Dom info

Recording the introduction to Apocalypse Please, Dom played a drum fill from the Grouse Lodge swimming pool, with a driver from an NS10 speaker used as close mic.
Whilst in the pool area, they decided to have a go at creating a water gong effect by hitting cymbals loads of times while dipping them into water. However, because cymbals have nowhere near the same sustain as an actual gong, the sound decayed as soon as they went into the water, which made the whole activity pointless!
Dom has a large floor fan next to him to keep him cool.