The following levels have secret exits.

World 1
Level 1-3: Leads to a cannon.

World 2
Level 2-4: Warp pipe directly to the castle.
Level 2-6: Leads to a cannon.

World 3
Ghost House: Leads to a cannon.
Level 3-4: Warp to level 3-5 or castle.
Level 3-5: Star Mushroom House.

World 4
Fortress: Leads to a cannon.
Ghost House: Star Mushroom House.

World 5
Ghost House: Leads to a cannon.

World 6
Level 6-5: Castle back door.
Level 6-6: Cannon.

World 7
Fortress: Warp to level 7-6.
Ghost House: Warp to level 7-5.

World 8
Level 8-2: Warp to level 8-7.