What email to use for corresponding author on publications when institution is not permanent?

It has become quite obvious by now that most researchers are on precarious employment for an extended period of time when starting their career.

As mentioned by Michael and Mark, it is very common to find gmail email addresses in scientific publications. I believe that nobody would find that objectionable.

Tips, anyway:

1. Do not use [email protected] but a variation on [email protected].
2. The issue of perenniality remains: GMail deletes inactive accounts after some time. Check their tools to address this issue: https://support.google.com/accounts/answer/3036546?hl=en
3. Self-hosted email (i.e. [email protected]) is also subject to cancellation if you don't renew your domain/email host.
4. If you maintain a web presence, your email will be easily findable in the future.

As a kind of "non-requested bonus", I would advise to register an ORCID and have your paper include it (most publishers will include it by now). The ORCID is a unique permanent researcher ID, see their website. On your profile, you can have a list of all your publications and also of your web page. You can include several URLs, meaning that you can list your current institution homepage, your personal hosted homepage, your google scholar account, etc. The ORCID page will be permanent, easily findable and you can update it.

EDIT: you can also list an email (at your preference) on your ORCID profile.

Many people I see use gmail by now, however, the majority still uses temporary institute email addresses despite losing it at some point - those who want to reach you will still find you, as long as you stay in academia.

One option would be to use a permanent alumni e-mail forwarding address provided by an earlier institution you were associated with, in particular the one you got your degree from.

Eg: MIT, Oxford ...