Free updates make the most sense. The revenue stream from payed Lion upgrades is laughable from Apple's perspective.
The only logical business argument one could imagine against the free upgrade would be that it lowers the perceived value of OS X in the eyes of the consumer. If it's free, that means it's not very good + it means it will always be free. Apple will never again get revenue selling OS X. But if you realize that OS X is not the product in this case (after all Apple doesn't sell OS X, Apple sells Macs) - this argument is no longer valid.
To all of you saying that 29$ is an OK price. Think about it. A customer who bought a Mac in 2007 and upgraded his OS 2 times for 29$ was spending below 15$ a year average on system upgrades. Now that number would almost double. So if they won't go with the free iOS model, they still would need to adjust the price and go down at least to 15$, or maybe even 9.99$.
But there are still more advantages to keeping ML free. It's a brilliant PR move. It's great for new OS adoption. It would be also solve the problem of people upgrading from SL vs upgrading from Lion.
In theory Snow Leopard users shouldn't have to pay the same amount for Mountain Lion, as Lion users, who already payed for one upgrade along the way. But on the other hand they shouldn't be forced to purchase both, because the total upgrade cost to go from Snow Leopard to Mountain Lion would be almost 60$ (provided they stick to their current OS X pricing) which is a pain.
Last time with Snow Leopard, Apple solved the problem with a license that required Leopard, but a DVD that didn't - which I guess made everyone happy (Tiger users got a 29$ upgrade to SL, and Leopard users got the peace of mind, knowing they didn't break the license agreement). But this won't be the case with the new digital distribution - they will have to figure out a new way to keep Lion users happy, and still give SL users an incentive to upgrade to Mountain Lion.
If the OS is free, it's a non issue. They could just keep both ML and Lion in the App Store. OS X Lion - available for 29$ to all Snow Leopard users, with Mountain Lion available free to all Lion users.
After that, they wouldn't even have to keep the OS in the app store. After Mountain Lion, the OS upgrade could just be part of the system update. That way they would get even faster adoption rates than with a free OS on the App Store (some users won't feel the need to upgrade, but they will most likely install anything that is a recommended update).
SO that's basically why Apple *should do it. But there are also people who seem convinced that Apple already decided against it. I don't think that's the case.
There was one big argument - the one about Apple anticipating future revenues from Mac users. First off, assumptions can change. Second off, Apple can get the revenue they want from Mac users in multiple ways, not just payed OS upgrades. They can get it from App Store cuts, iLife upgrades, iWork etc. Also the Messages beta text that says something about purchasing Mountain Lion is no proof against free ML. The way the App Store works, even if you download a free app, it's still referred to as a "purchase".
In general I believe it's good for Apple, it's good for developers, good for users, great for the Mac. Apple makes money selling hardware, they won't see a drop in revenue in the long term. This is a new world, people don't get as excited about OS upgrades as they did back in the days. They have multiple computing devices (iPhones, iPads), the PC is no longer the center of our digital life, so people don't see that much value in upgrading its software. Such a move would reinforce the notion that Macs are better suited for the post-PC world than regular PCs. That they will be better companion devices for your smartphones and tablets, because they will change along with them and you won't have to worry about paying for upgrades, deciding on new operating systems etc. Everything is just going to work together.