(Note: I started writing a broad answer of various methods to make strong encryption ineffective, rather than banning it outright, and their consequences... but it quickly got off topic. Then I realized that Tor talk basically covers the whole topic and has plenty of examples of encryption bans. Watch the Tor talk at the end.)
There are few examples of "banning cryptography" outright, and it doesn't last very long in this modern age because it basically shuts down business on the Internet. The ones I know of are usually done by totalitarian regimes in the middle of civil unrest.
In times a civil unrest, a government may assert their control over the Internet by partially or totally blocking encrypted traffic. That means SSL, ssh... anything using strong encryption. This cuts off a means of people communicating without fear of spying.
For example, in Feburary 2012, Tor reported that Iran was selectively blocking SSL traffic which also had the effect of cutting off Tor, a privacy network. Plus any number of attempts to shut down or filter the Internet as part of the Arab Spring.
This is often done through deep packet inspection, basically peeking at all the traffic going by and if you spot anything that looks encrypted you block it. This doesn't just happen. It requires a great amount of planning and design work to allow centralized control of packet routing and filtering. Even if it starts innocently enough, like stopping child pornography or terrorists, that very same system can be used to censor and track dissidents.
Tor is a privacy network within a network that not only encrypts your traffic, but it prevents listeners from knowing where it came from. This can mean life or death in a totalitarian regime who might come after you just for connecting to a web site they don't like.
Even using Tor can mark you as a suspect. Tor is in a cat and mouse game to look more and more like normal HTTPS traffic. This forces government filters who want to stop Tor to also hinter legitimate encrypted traffic. This causes businesses to be unhappy which exerts pressure on the government to stop fucking with the Internet. It's cutting off your nose to spite your face.
For more examples, watch How Governments Have Tried To Block Tor. It's fascinating and very informative overview from about 2006 to 2012.