You can use altmetrics alongside bibliometrics in any scenario where you are trying to demonstrate the value and impact of your work, such as proposals, personal websites, job applications and CVs.
Here are some examples of researchers using altmetrics:
Soressi, M., S.P. McPherron, M. Lenoir, T. Dogandžić, P. Goldberg, Z. Jacobs, Y. Maigrot, N.L. Martisius, C.E. Miller, W. Rendu, M. Richards, M. Skinner, T. Steele, S. Talamo, J.-P. Texier 2013 Neandertals made the first specialized bone tools in Europe. Proceedings of the National Academy of Sciences of the United States of America 110.35: 14186-14190. Open access http://www.pnas.org/content/early/2013/08/08/1302730110.
press release: Paper scored 27th out of the 19,867 PNAS papers in Altmetric score on 19th January 2014, which is our measure of the quality & quantity of online attention that it has received. (see http://www.altmetric.com/details.php?domain=www.pnas.org&citation_id=168...)
In a CV, above the list of publications:
Screenshot showing altmetrics used in a CV. In the Publications section of their CV, the author is linking readers to their profile on an altmetrics platform via a hyperlink which reads "ImpactStory profile for altmetrics data".