It's not at all unusual for the hiring process to take longer than a candidate would like, for all sorts of reasons: Decision makers are out of town, scheduling conflicts are delaying a final interview, the bureaucracy necessary to finalize an offer takes weeks to work through (not necessarily a great sign about the work environment, but that's a different topic), and so forth.
But you're not entirely at the company's mercy, although it might feel that way.
First, if the company didn't give you a sense of when it expects to make a decision, follow up to reinforce your interest and politely inquire about its timeline. If the interviewers did give you a sense of their timeline and that time has now passed, follow up and explain you're very interested but understand that hiring can take time, and ask if they have an updated timeline. Companies know that candidates may be juggling other interviews and pending offers, and they won't see this request as unreasonable.
Next, if you have time constraints, say so. For instance, if you have another offer, tell the first company's interviewers that you're extremely interested in the position but that you have an offer from another company that you need to answer within a week (or whatever your timeline is). Tell them that they would be your first choice but that you're constricted by the other company's timeline. Employers who are very interested in you will do what they can to expedite things.
(Of course, be prepared for them to tell you that they can't move any faster. That's one reason why you shouldn't play games with this, such as implying that you have another offer when you really don't.)
And whatever you do, don't let up on your job search, no matter how confident you are that an offer is coming. Things change; other candidates come along; plans for the position evolve or even get canceled. Until you have a firm offer in hand, you have to proceed as if you don't, since ultimately you can control only your side of the process—so keep setting up those other interviews.
And if you never hear back from the company—not even with a rejection (as seems to be a growing and incredibly rude trend)? That's a company you don't want to work for anyway. Bullet dodged.
Alison Green is chief of staff for a medium-size nonprofit, where she oversees day-to-day management of the staff as well as hiring, firing, and staff development. She is working with the Management Center to coauthor a book on nonprofit management. Her writings have been published in the Washington Post, the New York Times, Maxim, and dozens of other publications. She blogs at Ask a Manager.