EssaySnark says, actually, previous answer isn't quite on target. A bunch of bschools are very receptive to candidates straight from university. In fact, a bunch of bschools have programs where you can apply as a junior. These include schools on the OP's list - Harvard with 2+2, Yale with Silver Scholars, etc. - and so EssaySnark assumes you're interested in exactly those programs. These programs typically will accept students now for later matriculation, and in the intervening time, will offer extensive career services support to help kids get a job out of university, to work a year or two before coming to bschool.
The deadline for HBS 2+2 was about a month ago, and so if you're starting your final year at university this fall, you missed your chance for that program. However Yale Silver Scholars is still an option for you, as are several programs in Europe. Chicago Booth and UCLA are also known to accept early-career candidates into their standard MBA track. Not all schools do, so the other response is partly true, but there are more than a handful of schools that encourage apps from this younger cohort.
The point about leadership experience is valid, and that's what all these programs will be looking for: are you an overachiever? Have you made the most out of your university years, not just academically, but in really diving in and getting involved in the community, with your peers, etc.? Have you made some big contribution in the family business? What about internships? They'll look for evidence that you're a superstar in all these areas.
Harvard is trending younger every year; they have probably the youngest average age around, and are also open to getting apps from college seniors (standard program, not 2+2). You'll need to distinguish yourself on the GMAT and definitely need great academics. But there's a chance at a lot of bschools these days for younger candidates. You'll need to get started now and the GMAT is probably the first thing to tackle, since that score will determine whether or not these schools we're discussing are even in range for you.
