Buran and the Space Shuttle will not fly again. Both projects have ended, and the orbiters have gone to museums (or have been destroyed). Reactivating these programs would be enormously expensive at this point.
The Shuttle showed that a spaceplane has some disadvantages. It turned out to be really expensive to refurbish the spacecraft for each flight.
The Shuttle was designed for things NASA rarely or never used: the ability to launch, do something and then land one orbit later was never used. This ability drove the size of the wings, for example. The ability to retrieve satellites from orbit was used a few times, but not as often as envisioned.
There's a company working on a space plane right now (Dream ChaserDream Chaser), but it's much smaller than the Shuttle. If SkylonSkylon ever becomes reality, we could see a large space plane again.