Funny story, the basis for a majority of the sprites were created using simply MS Paint, which comes pre-installed on every version of windows.
We have since upgraded to Photoshop CC and sprite production has been made a breeze. CC introduces a lot of new features that make pixel art very easy to do, such as visible guidelines and pixel grids, and layering also helps us add armor or masks over our base sprites without any fear of messing something up. With that said, we still draw out each sprite pixel by pixel by hand, so it's a very time consuming process.
For the actual video side of things we use Flash CS5 and Flash CC, as well as Audacity and a powerful audio program called Reaper.