Just because your Mac has a folder that's meant for applications doesn't mean you need to put all your applications in there. "But why wouldn't I?" you ask. There are at least two good reasons to consider keeping your applications elsewhere:
You're not your machine's administrator
If you're on a machine owned and operated by somebody else — i.e., a work computer — you may very well have a legitimate reason to install a certain application, but you're unable to without the administrator's password. Strangely, the password only seems to be necessary when you move an application to the Applications folder, not when downloading or opening DMG files, not when opening an application for the first time, and not, crucially, when moving an application into any other folder.
(Obviously, you could just ask the computer's actual administrator to help you install any applications you need, too.)
You want to use the same programs across computers
Now that you're not installing to the Applications folder, Dropbox makes a logical alternate location. Assuming you have or can have Dropbox installed on all the machines you use regularly, installing to Dropbox acts akin to a USB drive loaded with a suite of portable apps. Rather than going through the install process again on a new machine, Dropbox will carry your essential apps over for you. I haven't had a chance to test this yet, but I believe if any of those apps store their data locally, rather than in the cloud, this will effectively allow you to keep your app data in sync across machines, as well. Handy!
Now, this won't work with applications that are downloaded from the App Store, and not with all programs that use an Install Wizard. (Remember those?) Thankfully, most of the marquee applications for Mac are still available in DMG format.
There may still be a few good reasons not to do this; notably, older versions of OS X had trouble recognizing apps kept outside of the Applications folder; this may still be an issue. It's also probably not a great idea to move already-established apps out of the Applications folder, for similar reasons.
That aside, I've been happily using Evernote and Portable Adium running off my Dropbox for months now, and have had no problems!