Are there any examples other than anomaly detection where unsupervised deep learning could be useful?
Recommendation Systems

In recommendation systems the idea of extracting signal and using to make recommendations is very common, e.g, Alternating Least Squares and Singular Value Decomposition approaches. 

Autoencoder fits quite well, reducing dimensionality (the encoder part) should help extract signal. The weights in the network represent the behavior of all the users that we trained on, but we don't want to capture all of it, we want to capture just the most import parts. Size of output of encoder (or bottleneck) controls the amount of dimensionality reduction.

Using it is quite simple:

1) You train the encoder-decoder model on, say, user movie ratings, where user ratings are input and output.

2) To generate recommendations for a user, just pass through user's current ratings through encoder-decoder, and you have the scores that can be used to make recommendations.