ImageNet, GoogleNet, etc. are all image datasets for precisely this purpose. There's also the recently announced YouTube dataset and Kaggle challenge [1] and Google Research's datasets [2].
I agree though, the kind of artificial / play-against-yourself datasets that the folks at DeepMind created for say Alpha Go are an entirely different beast.
[1] https://cloud.google.com/blog/big-data/2017/02/google-cloud-...
[2] https://research.google.com/research-outreach.html#/research...
Are there (artificial) datasets that can be used that showcase particular fit for deep learning?
I think there is way to little research in building artificial datasets (using domain knowledge of course).
It might even be possible to run these generative models and have this type of data very soon.