The strongest publicly available go AI is probably this: https://github.com/facebookresearch/darkforestGo, since there is currently no way to play AlphaGo. Is there any way to play this without building it on a local machine? Is it available on a server somewhere? Looks like the name on KGS is darkfmcts3 .
Hactar go https://play.google.com/store/apps/details?id=net.gowrite.hactarLite (android application) offers darkforest as opponent (darkforest running on server side). Not free, but 2€/3 month subscription.
(Edit: my answer is incorrect since these bots seem to have been taken offline).
There are a number of bots on kgs that run DarKForest that you can play against.
These are its accounts:
Playing against this bot on KGS is probably the easiest way for most people to play against it.