My short answer is that the 1-page resume is the only document which should be used in your job or school application (except for those positions that very explicitly ask for a detailed and complete curriculum vitae, usually involving lengthy detail on academic accomplishments). But that doesn't mean there is no use for a longer version.
I recommend regularly maintaining and adding to a 2-4 page resume, that is inclusive, and documents all of your positions and accomplishments. When you decide to apply for a job, or grad school, or anything else that requires a resume for that matter, then you can take this long resume and cut it down to a final 1 page version that is highly presentable because it shows a focused and strategic version of you. For the purposes of this article, let's call the long list of accomplishments the "master" resume, and the 1 page version the "finished" resume. There are several benefits to be had from such a system.
Benefit #1: You can keep everything, without having to show everything.
For many, it is hard to cut their 6th consecutive M&A deal from a resume, especially when they all seem to be so interesting! But the reality is that this level of duplicity is rarely necessary in a finished resume. So, keep the master resume as a comprehensive list, while the finished resume can be a more focused version that contains just those contents that are most relevant for the job or application. This is a great way to fulfill both urges people feel when they make a resume: 1) they want it to reflect absolutely everything, and 2) they want to feel that it is focused to the individual reader. It is hard to accomplish both with just one document, so don't even try.
Benefit #2: Content which is cut from the final version doesn't disappear.
I used to keep just a 1-page resume, and so when I decided to add something, invariably something else had to be cut. This is fine of course, but what if one of those cut accomplishments may have some level of value in a different, future situation? If all you are doing is continually refining and juggling the content in your 1-page resume, then once you cut something you may forget about it - and it may be useful later.
Benefit #3: The master resume can be easily adapted into a finished resume that is targeted for specific situations.
I've mentioned here that the finished resume needs to focus the reader's attention on the details of your background that are most relevant for them. Given this, a finished resume for your application to the MIT Sloan MBA program (where, by the way, they require a resume that is not "more than one page in length (up to 50 lines)", is not necessarily going to be the same resume you would submit for a job as a domestic sales manager at a fashion retailer. Your finished resume should instead be catered to fit each individual need to which it may be applied.
Note that as you finalize resumes for different purposes, you are not only cutting the volume of material so that it fits 1 page, but you may also be tweaking the word choice within bullet points to highlight different skills that you may aim to highlight for different purposes.
But why is it so necessary to make all of these painful cuts in order to arrive at my finished 1 page resume? Wouldn't a 2 page version just be easier to make? Why do I have to carefully go over all of my accomplishments in order to find just those key ones that are most representative of my skill-set, and that are most relevant to the reader? In asking these questions, you are giving yourself the answers: you need to make all of these decisions and evaluations of your resume content, so that your reader doesn't have to. Your 1-page resume is the movie trailer of (the relevant parts of) your life - it is short, to the point, and gets the viewer interested in wanting to learn more. Can a two-page resume do this? In most cases it can, but a one-page resume does it better, because it foes it more succinctly. There is a reason why movie trailers are only 2 minutes on average. It is not because there is anything wrong with a 10-minute trailer. The reason is because 2 minutes is all that it takes to make you understand, and get you interested in the story being told.
Here's a quick summary of the benefits of having a 1 page resume:
1) A 1 page resume offers the strongest initial impact, and makes it easy for the reader to quickly scan your background and be impressed.
2) A 1 page resume has only the most highly relevant and impressive content, because you have taken the time to select which bullet points to include.
3) A 1 page resume doesn't require the reader to go back and forth between pages or have to hunt for what they are looking for. Everything is laid out clearly.