Which email address should a student use in a publication?

It depends on many things, which I tried to order by descending priority:

• Possible journal policy: in most cases, they don't have one
• Possible employer policy: my own institution forbids the use of gmail.com addresses in lieu of our professional ones, because of a national policy forbidding use of commercial email providers for state-paid positions (prohibitions which my institution extends to students)
• Which email address you'll keep longer: students email is temporary, but gmail.com may also be (it may not be hard to imagine that, in some near future, you become infuriated by Google's (or any company's) behavior and close your account). On that note: if you graduated from some institution, you may get a permanent alumni email redirection, which may last longer than all those individual accounts.
• Which email looks more professional: [email protected] sure doesn't do any good for your reputation.

From personal experience, I have used my gmail account in the papers I have had published, without any hassles (in journals of impact factor 2+). I use the gmail account as it is one I still will be using when I complete my PhD, thus no longer have my university account.

Like with many things, it is dependent on the journal's policies - best to read up on what they expect, if in doubt, write and ask them. They may allow it, but it may be due to email addresses like gmail going to their spam folder.

Let me suggest a different direction (even though it doesn't directly answer your specific question):

Don't put your email address on the paper.

(obviously, put whatever you want for the correspondence when submitting the paper).

When I was a grad student, my advisor forbid me to put an email address for us on any papers unless it was required by the formatting guidelines. We just left out email addresses altogether, for the following reason:

If someone wants to find you, a simple Google search will turn up an email address that will be at least as current, if not more current, than the address on the paper.

"But what if my old website is still active with my old address?" you might complain. That's your own fault for not policing old websites. If you have switched institutions, your new website should quickly rise (or will eventually rise, anyway) above your previous sites, cached pages notwithstanding.

Will there be false hits because someone didn't find your up-to-date email? Sure. I'll argue that just as many times the email you put on the paper will be different than the one you currently use.

The fact is that email addresses change, and what you put on your paper may not matter in a year, or two, or twenty.