The Merlyn Morgan-Graham answer manages to delete the running batch script, but it generates the following error message: "The batch file cannot be found." This is not a problem if the console window closes when the script terminates, as the message will flash by so fast that no one will see it. But the error message is very undesirable if the console remains open after script termination.
John Faminella has the right idea that another process is needed to cleanly delete the batch file without error. Scheduling a task can work, but there is a simpler way: use START to launch a new delete process within the same console. It takes time for the process to initiate and execute, so the parent script has a chance to terminate cleanly before the delete happens.
start /b "" cmd /c del "%~f0"&exit /b
Update 2015-07-16
I've discovered another really slick way to have a batch script delete itself without generating any error message. The technique depends on a newly discovered behavior of GOTO (discovered by some Russians), described in English at http://www.dostips.com/forum/viewtopic.php?f=3&t=6491
In summary, (GOTO) 2>NUL behaves like EXIT /B, except it allows execution of concatenated commands in the context of the caller!
So all you need is
(goto) 2>nul & del "%~f0"
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