Can you activate a creature's ability the same turn it enters the battlefield if it doesn't have summoning sickness?

Summoning sickness (formally the 'haste' rule) prevents a creature from attacking or using activated abilities that include the tap symbol (T) or untap symbol (Q) in their cost, unless the creature has haste. This is defined in CR 302.6.

If a creature's activated ability does not use {T} or {Q} in its cost — for example, a mana cost like {2}, a life payment, or no cost at all — summoning sickness is completely irrelevant, and you may activate that ability the same turn the creature enters the battlefield.

CR 302.6 states: 'A creature's activated ability with the tap symbol or the untap symbol in its activation cost can't be activated unless the creature has been under its controller's control continuously since their most recent turn began.' Abilities without those symbols have no such restriction.

Concrete example: You play Llanowar Elves (which has '{T}: Add {G}') on your first turn — you cannot tap it for mana that turn because summoning sickness applies to its {T} ability. However, if you instead played a creature with the ability '{2}: It gets +1/+1 until end of turn,' you could activate that ability immediately the turn it entered, since no {T} or {Q} is involved.

So the answer depends on the ability's cost: if it uses {T} or {Q}, summoning sickness blocks it (unless the creature has haste); if it doesn't, you're free to activate it right away.