I see a lot of ideas that have already been done. For convenience, here's a list. Some are only possible with tweaking, so feel free to suggest tweaks.
Done as or fit as PvP Events
60-card decks
Lose to win
You are the Fake God
Done
Monodecks
Fate Egg/Mutation deck
Speed building
Mark change
Rainbow
The new (Gargoyle, Wings, Steam engine, Pandemonium)
My choice (TO selects elements allowed for each round)
No spells
Monodecks, same mark
Starter decks
The new (Forest Scorpion, Dune Scorpion, Deathstalker, Voodoo Doll, Nightmare, Short Bow, Mindgate, Chimera)
Three's a Crowd (max 3 copies of a card and max 3 elements in deck)
To the Skies! (at least 4 weapons of any kind and 4 flying weapon)
Cheapskate 5- (only cards with a cost of 5 or less)
Duality (only opposing Elements in a deck)
Creatures only (only one Element per round)
Speed-building
Quartets
Lazy man's game (no rares, no changing deck between duels)
Menagerie (only creatures and pillars/pendulums allowed, can only use one element once per round so you need 3 decks with different elements in each.)
Upped, Halloween (only aether, darkness, death, entropy, fire and gravity are legal, your mark must be one of those elements, no shields)
Upped, Rainbow
Upped, Creatures only
Upped, Trio decks
Mentioned and potentially feasible
Fractal decks only
Duo and trio decks only
No shields allowed
No more than 5 different cards in your deck.
No weapons besides Basic ones
No permanents besides pillars
Only Elements of specific colours allowed (fits with seasons/holidays)
Your decks may not cost more than X electrum to build.
No Healing cards
Only vanilla creatures
No creatures with more HP/Attack than X
New decks (ban the 2-3 or even more most used cards from each element - this could be either at the organizer's discretion or based on the (old) usage statistics)
Monodecks with only quantum pillars.
You must play the deck with mark that opponent used last game
Only creatures with abilities
Must use X amount of buffing cards
No rares
Deck size requirement as well as card number restriction
Must have X amount of Mutations/Elfs
Nymph Tears decks
Nymph Tears/Fate Egg decks
Must have X amount of Mindgate
Post deck beforehand and use only that
Dragons only
More cheapskates
Only Otyughs and buff cards
Must have X amount of Hourglasses/Precogs, possibly limit deck size
Each participant posts a prebuilt deck. Decks are then randomly distributed either for each round or all the tourny.
Max X amount of pillars/pendulums. No Immo/Nova
Your deck must contain at least one of every pillar.
Only X amount of card copies
Airborne only
Non-Airborne only (Wings banned)
6 Discords/Novas
Only 0-cost cards or random quanta cost cards
Creatures must be quinted upon play
No cards of your mark's Element
No perm control or Momentum
At least X amount of healing cards
Only Oty and low HP creatures
Only cards with an even cost allowed
No CC
Voodoo decks
No creature cards allowed (Nymph's Tears, Flying Weapon and Boneyards allowed)
Poverty (pillars, pendulums and quanta-producing creatures are banned)
Hexagon (precisely 6 copies of each card, including pillars and pendulums - e.g. either 6 or 12 lands)
A second chance (only creatures allowed are Gnome rider, Damselfly, Ash eater, Skeleton and Photon)
Must use the same deck through the whole tournament
Ye Olde Tournament (only allowed to use cards that were in Elements when it first began)
No creatures, no Fire Lance
Only one type of creature, no shields, rare weapons, creature generators or creature-creating cards
Be the Elder (max 4 copies of one card excluding pillars/pendulums, 1-3 rares, mark is set to most used quanta)
High price tourny (minimum quanta cost per card)