There is no risk in connecting the GND of the power supply and the RPi together - actually, to create useful circuits most of the time this is required so that the +9V from the power supply and the +5V/+3V3 coming from the Raspberry Pi are relative to each other on the GND.
Regarding the +9V power though, you need to make sure that this does NOT come into contact with the Pi (either directly or via a circuit you're making). It would likely blow up your Pi. What you can do is use a transistor or a relay, powered by the RPi, to switch +9V circuits on your breadboard.
Alternatively, you can just use the power coming from the RPi's GPIO output pins (3V3 signal level) to power simple circuits like those containing a few LEDs, just note that the maximum amperage the RPi can supply that way is 16mA per pin, with a total maximum over all pins of 50mA.
There are tons of good tutorials on the web (try Adafruit as an example) on how to start working with circuits on the RPi.