A lot of public key cryptography methods used in the real world are based on the fact that factoring really big numbers is computationally unfeasible. Shor's algorithm makes it feasible, but it's a quantum algorithm that can't be run on a classical computer. Basically, alot of stuff won't be secure anymore when it's feasible to run Shor's algorithm.

But would new forms of currently-infeasible encryption become possible at the same time? Many forms of encryption have fallen over the years as technology and mathematics have advanced; while at the same time better encryption methods have been developed.

Oh, of course. The dance between defense and offense will continue as usual. However, there may be a window of time where a lot of services are left vulnerable in the transition.