I can speak for magazine work. It's reasonable to expect to be paid in a month, although many will dither around longer than that. At that point, it's fair game to start with e-mails, "When can I expect my payment?" and rather than bugging an editor you dealt with, it's usually best to get the info for whoever cuts the check and deal with them. That way you don't compromise future work by being a pain in the ass to an editor who usually doesn't want to think about that stuff.
One thing I have learned. I now have a small business that does full-service custom publishing projects. I typically take money up front for things that are going to be printed. I realize you can't do that on freelance articles. But when I do send final invoices (and this is in any contract I sign for work), I always put payment terms on the invoice. It is typically "net 30 days." At that point, if it was the in the contract, it is legally fair for me to start charging interest (although I never have, because that is a great way to lose clients).
I very often wrote for magazines without signing contracts in advance, so I know what I am about to suggest is much easier said than done. But if you do sign any contracts in advance of doing the work, or you sign a stringer contract, it should have payment terms in there, saying the company will pay you within X days of receiving your work. Even if you don't have that contract for something you have done, when you send an invoice or even a simple e-mail that can function as any invoice, it's never a bad idea to put in payment terms, such as "net 30 days" They are probably going to ignore it, but it does make a statement that you expect to be paid in the time period just about every other business in the world does, and if they do reneg on payment, you are at least creating a paper trail demonstrating you made the effort to be paid within a reasonable time period.