An awful lot of people have internalized the old rule that your resume should be only one page and go through incredible contortions to keep their resumes down to that, even when they have years of experience.
The good news: The one-page-resume rule is dead. In fact, it's been dead for a while. Two-page resumes are common now, so if you've been agonizing over how to stick to one page, agonize no longer.
However, there's one big exception to this, and that's if you have only a few years of experience. If that's you, you should stick to one page. It looks a little silly to see someone two years out of school with a two-page resume; it's rarely needed, and you'll generally come across as a little self-important or unable to edit. There are exceptions to every rule, of course--but in my experience, everyone thinks they're the exception on this, when only a small minority of people really are. So be brutal about sticking to one page if your experience is limited.
What about resumes that are longer than two pages--three pages, four pages, or even more? I seen plenty of these, but I've yet to see a candidates who actually needed that third page. Even among very senior and experienced people, the best candidates stick to two pages because strong candidates know how to present their background and accomplishments concisely, distilling their experience down to what matters most.
Some people argue that they need those extra pages as they advance in experience and have more to write about, but there's no reason that your resume should be going into significant detail about things you did 15 or 20 years ago. Employers care most about what you've done recently.
(Keep in mind, of course, that we're talking about resumes here--not CVs, which are used in academia and Europe and which are longer.)
To be clear, resume length isn't on its own an automatic deal-breaker. If anyone is rejecting a candidate because of a resume that's a page longer than someone else's, that person probably isn't very good at hiring. But length does play into the overall perception of you as a candidate--can you convey essential knowledge quickly, do you know what is and isn't essential, etc.?--and that overall assessment is hugely important.
There's also another reason length matters: The longer your resume, the less likely an employer is to see the parts you want them to see. The initial scan of your resume is about 20 seconds--do you want that divided among three pages, or do you want it focused on the most important things you want to convey? Short and concise means that employers are more likely to read the parts you most care about.