Launching an app n minutes after boot up

Not directly, but you can do much the same thing by starting a script that will wait ten minutes, then launch the application. For example, with an AppleScript:

delay 600 --600 seconds == ten minutes

tell application "Dropbox" to activate
tell application "Something Else" to activate

Open AppleScript Editor in /Applications/Utilities and type this in. Then, save it as an Application, and add that Application to your log in items.

This will start the application(s) ten minutes after you log in rather than after when you start up, but your question suggests that you're automatically logging in on start up anyway. Starting Mac GUI applications genuinely on startup tends to not work.

[edit]Per Daniel Beck's suggestion, here's a way to do this silently:

Create the AppleScript described above, but save it as a script. Then create a Launchd property list. If you've installed the Mac OS X dev tools, you can use the Property List Editor that's included with them, or you can use a text editor (as it's XML). Create the following:

<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple Computer//DTD PLIST 1.0//EN" "www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
    <key>Label</key>
    <string>some.meaningful.name</string>

    <key>OnDemand</key>
    <false/>

    <key>ProgramArguments</key>
    <array>
        <string>osascript</string>
        <string>/path/to/your/applescript.scpt</string>
    </array>

    <key>KeepAlive</key>
    <false/>
</dict>
</plist>

Save this in ~/Library/LaunchDaemons/some.meaningful.name.plist. Then when you log in, your AppleScript will be run, though it will not provide an icon on the dock, which would allow you to cancel.