Ash is a particularly bendy wood and goes a long way before failing.
Hickory is another.
Many woods just wouldn't take that treatment, even if pre-bent or laminated. However, that is as much a function of design as it is of wood properties. For example, some designs manage to incorporate hinges in the longitudinal frame members so cleverly that hardly any bending of the wood is required. Of course these add their own weight and complication, but since they can also be arranged to reduce both the number of pieces of the frame and its packed length, their obviating the need for really springy wood might be considered just a nice side effect. To reply to the list, please hit the reply-all button and delete the original author.