Is Basalt Monolith a 1-card infinite combo with no payoff?
Yes, you can tap and untap Basalt Monolith arbitrarily many times, alone, with no other benefit.

The current text of Basalt Monolith's activated abilities is as follows:


  {T}: Add {C}{C}{C}.
  {3}: Untap Basalt Monolith.


The first ability adds three mana, and the second ability costs three mana of any type, so you can use the mana produced by the first ability to activate the second ability. Activating both abilities in order results in the game returning to the same exact state it was in before either ability was activated, so you can immediately do the same thing again.

The relevant rule for voluntary infinite loops, rule 721.2a says this:


  At any point in the game, the player with priority may suggest a shortcut by describing a sequence of game choices, for all players, that may be legally taken based on the current game state and the predictable results of the sequence of choices. This sequence may be a non-repetitive series of choices, a loop that repeats a specified number of times, multiple loops, or nested loops, and may even cross multiple turns. It can’t include conditional actions, where the outcome of a game event determines the next action a player takes. The ending point of this sequence must be a place where a player has priority, though it need not be the player proposing the shortcut.


Like with any infinite loop, you can announce that you are activating Basalt Monolith's first ability and then using the mana to activate the second ability any specific number of times.



A 2006 article on the Wizards website describes some previous power-level errata to Basalt Monolith that prevented this loop from working:


  This card had textbook power-level errata previously; it basically said “you can't use Basalt Monolith to untap itself.” I'm not sure if this clause was invented to stop combos with Power Artifact or the old wording of Relic Bind, but either way it was bad news. It is removed, and Power Artifact fans across the globe can rejoice!