Does a creature with vigilance still tap if you activate an ability that requires tapping it?

Vigilance is a static ability defined in CR 702.20a: it simply states that attacking does not cause the creature to tap. It does not grant any immunity to tapping in other contexts.

When you activate an ability whose cost includes the tap symbol ({T}), you are paying that cost by tapping the permanent (CR 602.2a). This is a completely separate game action from the process of declaring attackers. Vigilance has no interaction with it whatsoever.

So if a creature with vigilance has an activated ability like '{T}: Add {G}', using that ability still taps the creature, and it will be unavailable to block until it untaps, just like any other tapped creature.

Concrete example: You control a Llanowar Elves that somehow gained vigilance. You activate its '{T}: Add {G}' ability to produce mana. The Elves tap to pay that cost. Later in the same turn you attack with a different creature — the Elves cannot attack or block because they are tapped. Vigilance would only have mattered if you had tried to attack with the Elves, which would have left them untapped.

References: CR 702.20a (vigilance definition), CR 602.2a (paying activated ability costs including {T}), CR 106.4 (tapping as a cost).