If, for whatever reason, both players decide to keep flipping, the procedure from Game of Chaos could go on forever.
The joke card Mana Screw could go on forever (and presents some fascinating probability problems along the way)
Frenetic EfreetFrenetic Efreet can be used to flip an arbitrary number of coins (although you have to decide how many you will flip before you start flipping). This can be used to (probably) win the game with Chance Encounter.
Shuko and the en-kor have abilities that can be repeatedly activated and target a creature. This single-card loop can be combined with Cephalid Illusionist to mill yourself, and win through a set of other cards like Narcomeba and Dread Return (see the Cephalid Breakfast deck).
Aphetto Alchemist, Seeker of Skybreak, Tidewater Minion, and Basalt Monolith all have abilities that can repeatedly cause a permanent to become untapped. This single-card loop can be combined with Wake Thrasher or Mesmeric Orb (if you want to mill yourself) for profit.
Honorable mention: if your lands tap for more than 1 mana (or you have a land that taps for enough mana, such as Sanctum of the Sun or Nykthos, Shrine to Nyx), Palinchron can be returned to your hand and played repeatedly.
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