[philosophyguy]

Chase: perhaps there's a creature that steals something from a PC, or a horse bolts away, or an ally is captured.

Recover the gear: the party loses a signature item (e.g., fell through a crack during an earthquake) and the group needs to explore and retrieve the item.

Puzzles: a part of the dungeon has a puzzle that the PCs must solve in order to advance. Logic puzzles and riddles both work, in different ways.

Stealth: the party needs to sneak into and out of an area without being detected, possibly while doing recon or sabotage.

Stop the ritual: the PCs must disrupt a ritual before awful things happen.

Escort mission: the PCs must keep an NPC safe through a travel sequence.