Does vigilance prevent a creature from being tapped by an opponent's spell or only from combat?

Vigilance is a static ability defined in CR 702.20a: "Attacking does not cause this creature to tap." That's the full scope of the ability — it only exempts the creature from the rule (CR 508.1f) that requires a creature to tap when it's declared as an attacker.

Vigilance does nothing to protect a creature from being tapped by spells, activated abilities, or triggered abilities. If an opponent casts a card like Paralyze or uses Azorius Guildmage's tap ability targeting your vigilant creature, the creature is tapped normally. Vigilance simply has no interaction with those effects.

This matters because a tapped creature, regardless of how it became tapped, cannot attack (CR 508.1a requires a creature to be untapped to attack) and cannot block (CR 509.1b requires a blocker to be untapped). So your opponent can effectively remove a vigilant creature from combat by tapping it through a spell before you declare attackers.

Concrete example: You have a Gustcloak Savior (a creature with vigilance) untapped. Your opponent activates Icy Manipulator targeting it. Gustcloak Savior becomes tapped. It cannot attack or block this turn — vigilance does nothing to prevent this, because vigilance only applies to the tap cost of attacking, not to outside tapping effects.