We've installed a number of fold up seats like the ones shown to the upper right. There are some advantages from using a fold up seat over a fixed or built-in seat. Fold up seats take up less room, are less expensive to install vs. constructing a fixed or built in seat. Plus the wood seat is warmer to sit on then tile or stone.
One thing to keep in mind is that good structural support or blocking needs to be in place behind the shower prior to installing any kind of folding seat. It may be possible to install the blocking behind the shower from an adjacent room. Consult your local remodeling professional to see if this is feasible.
I recently discovered in one of my professional trade magazines, the Serena Seat which is pictured to the right. It's clean look and ease of use had an immediate appeal. It's easy to install on a properly prepared shower wall and has a back rest to lean against. When folded up it only has a 3-inch profile. It also has a precision tension hinge which prevents the seat from accidentally falling down. The wood is brazilian walnut which is up to 3 times stronger then teak.