Windows respects the process ACL, and by default, this allows access to the user the process is running as as well as to the local system account and the user's logon session SID. Administrators can bypass this ACL using SeDebugPrivilege.
Otherwise, you would need to be an administrator in order to debug your own code.
You can change the process ACL, but since normally (IIRC) the current user is the process owner I'm not certain whether or not you can prevent another process in the current user context from changing it back. Also, since it is likely that the processes are running on the same desktop, you would be subject to shatter attacks anyway.