Can you activate a creature's tap ability the same turn it enters the battlefield without haste?

A creature is affected by what players commonly call 'summoning sickness.' Under CR 302.6, a creature cannot attack and cannot use an activated ability that includes the tap symbol (T) or untap symbol (Q) in its cost unless it has been under your control continuously since the beginning of your most recent turn.

This restriction applies specifically to abilities that cost a tap or untap — it does not apply to other types of abilities. If a creature has an activated ability with a mana cost or another cost that doesn't involve tapping itself, that ability can be used freely the same turn it enters the battlefield.

Haste (CR 702.10) is the keyword that overrides summoning sickness. A creature with haste can attack and can use tap/untap symbol abilities the very turn it enters the battlefield, as if it had been under your control since the start of the turn.

Concrete example: You play Prodigal Pyromancer (which has '{T}: deal 1 damage to any target') on your turn. Even though you could theoretically use the ability, you cannot activate it this turn because the cost includes T and the creature just entered the battlefield without haste. You must wait until your next turn.

Note that this rule only applies to the controller of the creature. It also only restricts tap/untap-costed abilities — triggered abilities or static abilities on the same creature are completely unaffected by summoning sickness.