I've been using Adobe Audition 1.5 on a Windows XP machine. I happened to notice in the Task Manager that Audition.exe seems to an active process most of the time and uses about 13MB of memory -- even when the app isn't running at all. To the best of my knowledge, nothing should be constantly running in the background. Any thoughts as to why this might happening?

Because adobe makes bloated bloated software.
One way to disable it would be to go to start>run> type in services.msc

On that screen find the adobe entry and right click it and choose properties. Then set its start up type to manual.
That way it will only open once you have opened audition.(you will still have to disable it each time you use it)

Just what do you mean by "disable it each time you use it?"

When you start up audition that back ground service is going to start up.
Its not going to go away until you close it. At least it isn't going to run at windows start up anymore though.(if it was.. I don't use it)

So how do you go about closing it? Can you use "End Process" in Task Manager?

yeah thats what I would do..