Spontaneously reopening apps at startup
By default, when you restart your Mac, OS X 10.7 Lion and later reopen whatever applications and documents were open when you shut down. Whether this happens depends on the decision you make when you choose Restart or Shut Down from the Apple menu. In the dialog box that appears, if the 'Reopen windows when logging back in' checkbox is selected, the items will reopen; if not, not. However, you must make this decision before you shut down or restart, and it's all or nothing—if you want to open only specific items, you'll have to uncheck this box and add the items that you want to open at login to Login Items.
Other explanations for mystery processes
Although the methods I've mentioned so far are the most common ways to launch apps automatically in OS X, they aren't the only ones. If you have a mystery process that you can't track down in any of these places, it could also be one of these:
A kernel extension: Kernel extensions, or kexts, live in /System/Library/Extensions and load at startup. They provide low-level features such as processing audio and adding support for peripherals. Most kexts on your Mac are part of OS X. The safest way to remove a third-party kext is to run an uninstaller provided by the developer.
A cron job: Cron is a Unix scheduling utility built into OS X. The easiest way to view and edit cron jobs without using Terminal is to download the free Cronnix utility by Sven A. Schmidt.
A login script: Login scripts, like startup items, were used in older versions of OS X but are now deprecated.
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