Internet: crowdfunding, crowdsourcing, crowd-anything that challenges traditional top-down and institutional choke points.
Energy: General Fusion, Helion, and other alternative fusion startups exploring other idea... I feel that the tokamak eats all official R&D funding in this area (and boy can it eat funding). Also a whole gaggle of energy storage startups... grid-scale storage is the missing piece to make renewables really work.
Space: SpaceX, Firefly Space, Blue Origin (debatable whether it's a "startup" or Bezos' pricey side project), Sierra Nevada (not quite a startup but doing new things), etc. (Might even throw in Orbital Sciences, which is a "startup" by average age of aerospace company standards).
Biomedical: Immunity Project, anything in SENS / life extension.
Overlaps quite a bit with old Leary's ideas about priorities...
http://www.futureconscience.com/smi2le-the-futurism-of-timot...
Guy was a bit nuts, but the good kind of crazy.