Logging on as a logon with sysadmin Server roles and executing the following sql statement:

 select * from sys.sysprocesses

will return sysprocesses of all users on the server.

Logging on as a logon with with db_datareader permissions on a database and executing the following sql statement:

 select * from sys.sysprocesses

will only return the users process.

This is because, if a user does not have VIEW SERVER STATE permission on the server, the user will only view their own session.

The syntax to grant permission is

GRANT VIEW SERVER STATE TO user

Republished from http://www.sqlserver-dba.com.