Specialized tools for building robots
Getting into electronics does not ask for an oscilloscope. But if you are serious, invest on a good oscilloscope (be informed that they don’t come cheap). Also known as scope, CRO, etc. this device is the most useful instrument available for monitoring varying signals plotted on a two dimensional screen with X-axis representing time and Y-axis plotting the potential difference. They also double up as a quick and easy debugging tool for your circuits. If you take my words, invest on a good Oscilloscope and you will never repent.
A function generator (a.k.a signal generators) is a device which produces various patterns of voltage at different frequencies and amplitudes. The output from this device can be a square wave, triangular wave, sine wave etc.
Electronic component cabinet
Electronic parts like resistors and capacitors pile up soon and it would be difficult to manage them. Get an electronic component cabinet where you can store all the components in the small plastic boxes inside. Few cabinets also have storage areas to keep all your tools and devices.
More sophisticated devices
Long term robot interest might push you to invest in CNC machines, Lathe, milling machines etc. These are not really required if you take robot building as a hobby and build only a few robots in your lifetime. But if you wish to make your own brackets, chassis, robot parts etc. then getting these bulky machines would be an added advantage.
Tools are there to ease your work and most of the time you can do away without using them. But if you prefer to spend more time on designing your robot than construction, it is better to include them in your list.