There are two ways this could have happened.
One way is that you were prompted to install Growl and you approved that installation. Either you didn't read the dialog box or you hit the wrong button; either way, you installed Growl without meaning to.
The other is that something installed Growl without your permission.
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We distribute a framework to application developers to make it easy for them to use Growl in their applications. They don't have to write all of the pages of code necessary to send messages to and receive messages from Growl; they simply drop in our framework and write a few lines to tell the framework what to do.
We currently offer two versions of that framework. One of our frameworks does not and cannot install Growl. Our other framework will offer to install Growl the first time the application tries to send a Growl notification.
The key phrase there is offer to install. Our framework, when developers use it according to our instructions, asks for your permission before installing Growl, and won't install Growl if you refuse. You can also tell it to go away and not ask you about Growl again.
However, there are a couple of applications that bypass our permission check, or don't use our installer framework in the first place, and install Growl without your permission. Let us be clear: We do not endorse applications installing Growl without your permission. In fact, we hate it.
Nothing should ever install anything on your system without your knowledge and your explicit consent.
This is a list of applications that we know install Growl on your system without your permission, along with our notes.
Dropbox is the first application that we were made aware that installs Growl without your permission. We questioned their Team, and found out that they did this because in their opinion it helped with the usability of their installation.
Upon discovering that Growl has been installed, some users decide to remove Growl, and are then surprised to find that Growl gets reinstalled. This is because Dropbox installs Growl, if it isn't already installed, every time you launch Dropbox (which you may have set to happen when you turn on/log into your computer) when Dropbox's setting to use Growl is turned on, and that setting is on by default.
Instructions on how to uninstall Growl and set Dropbox to not reinstall it are below.
Adobe has an article in their knowledge base explaining what notifications CS5 sends and how to remove Growl. They have also published a blog post all but apologizing for installing Growl on users' systems without permission, and saying that they are “actively working to mitigate the problem”.