We have wide range of microcontrollers for your robotic projects. They are often considered as the brain of a robot and are usually the only piece that can be programmed, at least on simple robots. You will probably have to decide whether you want to work with a proprietary or open source microcontroller architecture and/or with proprietary or open source code library.
The board will come with a variable number of input/output connectors (from simple pin to USB connector for instance). The number of sensors or actuators you have to connect to your microcontroller should be one of the criteria to find out the best device for your robotic project. Some additional components like LED, USB cables, wires, etc... may be useful for testing and debugging.