Is it necessary to obtain permissions for copying figures from published articles in your proposal/dissertation? I am currently writing a proposal for my research topic and I want to copy figures from published articles into my proposal document. To put it in perspective, almost all the copied figures are to go in the “Literature review” section of the document. 

Is it necessary to send an email to each and every author requesting permissions to copy the figures, even though complete citations and references are included? I referred to the following link:
MITLibraries: Reuse of content in thesis.
From what it says, copying images in thesis (with correct citations) seems to be valid under US copyright law.
For figures from your own papers, it would depend on the copyright transfer agreement you (or the corresponding author) signed upon publication. However, all copyright agreements I know explicitly authorize reuse of content for academic theses.

As an example: the American Chemical Society, which does not leave the authors too many rights, includes this wording:


  Authors may reuse all or part of the Submitted, Accepted or Published Work in a thesis or dissertation that the Author writes and is required to submit to satisfy the criteria of degree-granting institutions. Such reuse is permitted subject to the ACS’ “Ethical Guidelines to Publication of Chemical Research"




For figures from others’ papers, a thesis is not very different from any other publication (see the related question about blogging). Unless your institution has a specific agreement with publishers (as MIT seems to have), you have to either:


ask for permission; these days, it's all done online and once you have located the appropriate form for a publisher, you can make your requests and get all the answers the next day
rely on fair use in the US, or similar law in other countries; around me, most people actually do that, either knowingly or just out of ignorance :)