Though many components for a serious robotics project will almost certainly have to be purchased, the total cost of the project can be reduced by harvesting parts from various electronic and electro-mechanical devices. The general rule for selection is "the older, the better," as newer devices are now dominated by specialized ICs and surface mount components that builders might find difficult to use in their robots. SMD (Surface-mounted devices) can be used to create very small robots, if one has the tools and patience to work with them.
An example of a good source of parts would be a printer from the 1980s. Without even disassembling such a printer, one can see all sorts of potentially useful components. Additionally, several metal rods and plates contained in the printer may be used as structural parts for the robot, and even the plastic case itself could be used.
Old floppy disk drives and copy machines are also good sources for parts such as stepper motors, optocouplers or microswitches, regular components, machined metal rods and hardware. Hard disk drives have fewer usable parts but can still be a source.
However stepper motors from printers and copy machines tend to consume a lot of power and may not be as good for battery operated robots.
Note to potential contributors: perhaps there could be a "case studies" section here, with examples of what can be obtained from a variety of devices.