Mark was quickly pointed to the System Profiler (accessible from the Apple Menu - About This Mac - More Info), which has the list of applications on your system.
I don’t really like the DMG part of the process, not to mention that many software publishers muddle it up by putting it in a ZIP file or some other layer of complexity (Apple should make sure that DMG files have solid compression, so that developers would see quickly that they save next to nothing by compressing it further). The idea is to parallel installation media for downloaded software, of course. It’s the software equivalent of the installation CD-ROM, and it does a pretty good job of behaving very similarly (I think you can even burn a DMG more or less directly to a CD-R).
But the actual dragging of the application I think is just fine. “Normal” users don’t necessarily get the “installed” or “not installed”, how to put things in the Start menu, and so on. On Ubuntu, I really like installing packages (I was already familiar with APT), but if I don’t like the way things are in the menu, it’s not completely obvious how to fix it. The entry in the menu isn’t really the application, but a shortcut.
On the Apple, there isn’t two entities like that for most applications. The “thing” you double click on is all there is. It was on the installation media. You can move it wherever you want, just like any other “thing” (be it document or other, using drag and drop or whatever method the user is comfortable with, since they behave like everything else). Apple suggests putting everything in the Applications folder, because it’s easy, but if you want to pile everything on the desktop or in your home directory, you do as you want. The shortcut is never confused, by the virtue of not existing. And when you want to get rid of it, you delete it like any other “thing” on your system, using the way you’re comfortable with (I like Command-Delete, myself, since I navigate the Finder with the keyboard).
It makes the application something no more mystical than a document that the user could have created himself. You have a freeware that you want to give to one of your friends? Easy, you just make a CD with the application on it, then give that CD to your friend (the same process that you would have used for a user document).
It’s definitely a different compromise, and it has its downsides.
In a more corporate setting for example, I would vastly prefer APT, over both the Windows way and the Mac way. But for a “normal user”, this has its downsides as well. For example, installing software that is not available in Ubuntu’s package manager is a world of pain. At best, you could add a third-party repository to the package manager (which would also keep it up-to-date), but that’s not exactly simple, and it’s not the kind of thing you’d do for a random application from the Internet you just want to try out (then you’d have to remove the repository, etc). It also doesn’t work all that well for commercial applications installed from a CD, for example (it does work, but it’s definitely off the beaten path again).
Ubuntu has control over what goes in their standard package repositories (even the “universe” stuff, even though they don’t package it themselves), but people trust them enough for that at the moment. Apple would have a harder time doing that, and I wonder how well would Adobe’s Lightroom fare compared to Apple’s Aperture in a “virtual showroom” la iTunes Store, for example. And can you imagine the call to arms there would be if Microsoft had such control?