Can I cite email communication in my thesis/paper?

The exact manner of how you should cite the communication may vary from style to style (often the date is included), but it's entirely reasonable to cite such a communication in a paper or thesis. Typically this is referred to as a Personal Communication. Obviously, wherever possible, you should look for information in published sources, but where this is not possible citing such a personal communication will suffice.

From memory, I think there might be one in my own thesis. A specific detail of an experimental method used in a published article was not discussed, but I thought it relevant to my argument so I contacted the author to get the information I needed.

Edit: Typically personal communications should not be included in the reference list as they are not evidence that can be readily recovered by anybody reading your work. This is made explicit in several prominent styles (e.g., Harvard, Chicago, APA).

I would strongly advise against citing personal communications without express permissions (written or oral) of their authors.

As far as I understand, e-mail correspondence is deemed confidential "unless noted otherwise". For example, I often share my unpublished results with trustworthy colleagues . If they broke my trust, somebody could scoop the results.

Let me give you another reason. I believe people are much more casual in their e-mail than, say, in their journal articles, they do not check them as thoroughly, so they may be unhappy about their casual thoughts being published as their opinion without their permission. By asking their permission, you give them an opportunity "to think twice" about airing their views.

Maybe I should add an example. Some time ago a colleague disclosed my age in a forum. He had obtained the information from my e-mail. It is not that I hide my age, but neither do I publicly advertise it, so I had to reproach him for disclosing my personal information.

This is called personal communication and can be (and is occasionally) cited if no better references are available. There is nothing wrong with something like this (and it is certainly not impolite):

Method X (Smith et al., 2015) can very efficiently solve problem Z provided a number of prerequisites are fulfilled, but it cannot be applied with Y (Smith, personal communication, 2016).

References

Smith, Jones, Snyder (2015): The great method X, Nature, ...

Adjust to your citation style, which should have a template for personal communications.

Obviously, it would be better if you could elaborate on why it can't be applied with Y. Then you would not rely only on the personal communication.

Note that some journals ask for written permission from the person who is quoted [1]. It would also be polite to ask for this permission.