Processor
A large part of the robots design is driven by the main processor. I'm using a low-power 12V mini-ITX board because I already have one. It supports various operating systems, wired and wireless networking, Bluetooth via a USB dongle and pretty much anything else I want to add via the USB ports. It draws about 15W of power. It has some solid state storage and a large hard disk. It is also easy to program and develop on. It's also got enough processing power for complex tasks and autonomous operation.
Operating System
I'm currently running Ubuntu LINUX on the mini-ITX and it seems to support everything I need to do.