With most applications status available online, follow up or not?
A single polite e-mail after a respectful amount of time (which varies greatly depending on field and whether you're talking about paper review or job application) is not likely to hurt you. Badgering, demanding, and aggression are likely to hurt you.
Admissions and job hunts are probably the places where you might consider a follow-up e-mail as a way to demonstrate continued interest.
With a journal submission you might send an e-mail if the editor is clearly &quot;sitting&quot; on the paper, or the status hasn't changed in some long period of time (2-3x the typical review cycle for that journal, for example). But in my case this kind of e-mail almost never yields a useful result except to have the editor write back &quot;we're still waiting on reviewers.&quot;
For a grant application there is zero chance that this will help you or yield any useful information. There is usually no information until all of the information is publicly available and you can't do anything except sit back and wait.
So, to possibly try and get a general trend here: the utility of a follow-up e-mail is inversely proportional to the size of the organization you are e-mailing. For a small research group or company where only a few people are likely handling all of the applicants for a job posting, it might be helpful. For a governmental organization of 1,000s of people with a highly codified way of doing business (or possibly even laws regarding transparency), an e-mail is just shouting into the darkness.