We have Amazon Prime, which is nice. We also have HBO Go and watch all HBO online. There is another HBO option if you don't have cable TV that is $5 more a month ($20 total, I think).
We go to the network websites to watch current content on-demand.
Roku does well for a number of other networks online. Hulu is another option.
I tried watching PBS online for things I missed on regular PBS TV and they wanted me to become a paid subscriber to be able to do that.