Does a creature that becomes tapped during combat still deal combat damage?

Generally, yes — a creature that becomes tapped during combat still deals combat damage, as long as it was already legally declared as an attacker or blocker. Being tapped is the result of attacking, not a barrier that removes a creature from combat once it is there.

When attackers are declared, attacking creatures become tapped as part of the attack declaration process (CR 508.1f). After that point, the creature is already 'in combat.' Tapping a creature that is already attacking or blocking does not remove it from combat and does not prevent it from dealing damage (CR 506.4).

However, if a creature is tapped before it is declared as an attacker, it cannot legally attack at all (CR 508.1c requires attackers to be untapped). In that case it never enters combat, so it deals no combat damage — but this happens before combat damage, not during.

Concrete example: Your 3/3 attacks and becomes tapped. Your opponent responds by using a tap effect (e.g., a creature with a tap ability) on your attacker. Your 3/3 is already tapped from attacking, nothing changes — it is still in combat and will deal its 3 damage during the combat damage step.

The key rules are CR 508.1f (creatures tap when declared as attackers), CR 506.4 (creatures remain in combat until removed by a specific effect), and CR 510.1 (each attacking/blocking creature deals its power in combat damage).