Databases:
- PipelineDB
- Snowflake (Computing)
Internet of Things / Communications:
- Helium
Robotics:
- Pneubotics
- Kuka, namely the research department
Autonomous Systems / "Self Driving Car" et al.:
- Kiva
- Anki
Computer-Vision / VR based:
- Jaunt
- Oculus VR (especially the 'research' department)
Agriculture:
- Blueriver http://www.bluerivert.com
(there are many more super-interesting companies in this area!)
Computing:
- Mill Computing; though quite dubious
- D-Wave
and than there is Microsoft Research working on super interesting stuff in programming languages, computer architecture (FPGAs).
Additionally, I believe really challenging problems will alwyas be coming from creative people, companies in that area; such as Pixar, architecture, and design (keywords, just to give a start: generative {design, art, ...}).
Hope this helps!