Nengo supports both supervised and unsupervised online learning. You can build your networks with the different forms of learning by using different learning rules. Included in Nengo is the PES learning rule, which is a online supervised learning rule, as well as the BCM and Oja learning rules, which are online unsupervised learning rules. Nengo also includes other learning rules, which are described here. There is even an (super rough) STDP implementation described here and here (STDP is an unsupervised learning rule).
The cool thing about Nengo is that it is general enough to users to implement their own custom learning rule, be they supervised or not! 