Highest possible power of a creature
Arbitrarily large.
It's not that hard to create a combo with a small number of cards that increases a creature's power without bound.
For example:

Pili-Pala
Grand Architect
Ghave, Guru of Spores
Doubling Season

The first two create infinite mana (use Grand Architect to make Pili-Pala blue, tap Pili-Pala for {2} with Grand Architect's ability, pay those {2} and untap Pili-Pala for 1 mana of any color, and repeat). Then you can pay {1} and remove a counter from Ghave to put 2 tokens into play (due to Doubling Season), then pay {1} and sacrifice one of those tokens to put 2 counters on Ghave (due to Doubling Season). The end result is an arbitrarily large number of +1/+1 counters on Ghave and an arbitrarily large number of tokens.
Keep in mind that you don't need infinite time (or even O(n) time) to give a creature arbitrarily large power, using this combo or just about any other. The Magic rules allow players to take shortcuts, as described in rule 719. The specific rule that is relevant here is 719.2a:

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.

Example: A player controls a creature enchanted by Presence of Gond, which grants the creature the ability “{T}: Put a 1/1 green Elf Warrior creature token onto the battlefield,” and another player controls Intruder Alarm, which reads, in part, “Whenever a creature enters the battlefield, untap all creatures.” When the player has priority, he may suggest “I’ll create a million tokens,” indicating the sequence of activating the creature’s ability, all players passing priority, letting the creature’s ability resolve and put a token onto the battlefield (which causes Intruder Alarm’s ability to trigger), Intruder Alarm’s controller putting that triggered ability on the stack, all players passing priority, Intruder Alarm’s triggered ability resolving, all players passing priority until the player proposing the shortcut has priority, and repeating that sequence 999,999 more times, ending just after the last token-creating ability resolves.


Obviously, the example they use isn't exactly the same, but it means that I could do the same thing with the combo I described by saying &quot;I'll create a million tokens and put a million counters on Ghave&quot;