Always use your institutional (academic) email address on your cover letter, and when contacting the Editor. Why does this matter?
Editors have become suspicious of authors who use personal email addresses because of recent scandals with bogus submissions; see, for example, this article in the Washington Post on a peer-review ring). If you have to recommend reviewers, do not use their personal email addresses either, as the Editor may also be suspicious that these are not genuine reviewers.
If you are likely to move during the review process, you could add a line explaining the situation, e.g., “The research was carried out at the University of X. I am in the process of moving to the University of Y; until I receive my new institutional email address, please contact me at email@example.com.” Alternatively, appoint another person as the corresponding author to avoid this problem.
One final point: if you do have to use a personal email address, don’t use the one with the funny name that you set up when you were a school student. The editor might not find it so amusing to send an email to “miss_cute_kitty.”