As Pekka mentioned, this was first discussed fairly early in the site's development on the podcast:
We will never make you log in and create an account to do things. That's one of the things we kinda took out of Wikipedia, was that we wanted to make it sort of egalitarian.
Another sorta subtle difference is, on every question page, there's a box at the bottom inviting you to participate. You don't have to click through to another page, or do another thing, there's just a text input box and it's inviting you to participate by answering a question.
That is the unit of work on our site - asking and answering questions. You can log in - with your OpenID - or, there's your traditional "blog comment" name, email, homepage, and you can just type in whatever you want there and post an answer without having created an account.
(edited - full transcript available here)
Jeff goes on to reference Jan Miksovsky's classic blog post Hurdles at the entrance to a site, which describes the ridiculous amount of resistance most sites impose upon people who don't even know if they want to use the site yet.
With all these hurdles, it's a small miracle some web-based services end up with any users at all. Each hurdle constitutes an opportunity for the user to leave. The site is effectively asking the user, "Are you sure you want to use us? Are you really sure? How about now? Are you sure you're sure? Hmm?" Some users are going to take one of these opportunities and leave. People are growing increasingly leery of starting down the hurdle-strewn path of a new site. They've been down similar paths so many times that they've concluded the experience won't be worth their time unless they're already confident the site will provide substantial value.
Note that eventually Stack Overflow reached a level of traffic that made it prudent to impose this extra bit of resistance on people here just to ask questions. As you can probably surmise, one of the downsides of making it really easy to participate is that a lot of folks end up doing so when they clearly have very little interest in doing so positively - but the "cons" don't end there. If you listen to the podcast, you'll see a few of them called out early on, but here's a more comprehensive list:
Because the site is so usable with so little effort, many folks forget that they didn't create an account. When they try to log in later, with whatever credentials they thought they might've used, frustration results.
If you don't enter a valid email - or lose access to it later - there's no good way to regain access to an unregistered account if you lose your cookie.
If you don't care about reputation or the privileges that come with it, it might be easier to just keep creating new unregistered accounts by participating anonymously and clearing cookies. This can be done for malicious reasons, or just out of laziness... But even when the participation is largely positive, it can be confusing to other readers. We don't focus too much on social interaction here, but it is important - it's nice to be able to recognize someone who often posts good or bad answers.
Some privileges depend on having a stable account. You can always comment on your own questions (or on answers to them), but if you lose the account you used to post the question then you lose this privilege. Same goes for editing and accepting answers.
Speaking of privileges, unregistered users can't vote. This is intentionally done to prevent abuse, but it does tend to reduce the signal generated by folks who could otherwise be providing valuable feedback on the posts they're using.
Even on Stack Overflow, we still see the potential benefit of encouraging people to answer questions sufficient to outweigh the downsides of transient accounts. We're always working on making the transition from one to the other easier though.
First off, very few people use their "real" names on a regular basis, where "real" means legal first name + last name. In some cultures that isn't even a normal construct, but even in the US how often do you really identify yourself or address others in this manner? The truth is, you probably travel, conduct business, volunteer in your community, worship and hang out with family or friends on a regular basis without using your full, legal name... And much of this you probably do without using a name at all.
So you're attacking this from the wrong angle, assuming that a "real name" policy would somehow be the default and a system that allows anonymous or pseudonymous participation is a conscious deviation from this. It's not. Implementing and enforcing such a policy is difficult and can easily cause more problems than it solves - particularly when using an externally-identifiable name is likely to be of more potential value to the author than to others on the site.