As noted- depends on the aircraft. PA28-180 OK, PA28-151/161 not OK. C172/182 OK with appropriate placard and limitations (Max Vno, Max 30 degrees AOB?) - numbers from memory don't quote me!
Interestingly C150 is approved but C152 not - a bit of data that was not transfered in the type certificate as far as I can tell.
Most light twins with a foward/crew door not ok due to control issues. Aircraft with rear doors usually approved with limits- depends if anyone has used it for parachute ops etc already.