Operation: Rusty's Blanket is a mission given to the OSI that was first assigned to Myra Brandish, and then after her subsequent removal it was assigned to the current agent, Brock Samson. Molotov Cocktease also worked on the operation for a brief period of time, although she was Brock's stand-in, rather than an agent being assigned by the OSI.
The mission itself seemed simple, and was presumably to protect Dr. Venture (a.k.a. Rusty) from any and everything harmful. Essentially the agent assigned to the operation appeared to be there to do little more than act as Dr. Venture's personal bodyguard.
The Truth Revealed
During the events of Orb, it was revealed that the acronym for Operation Rusty's Blanket, ORB, was its real mission. Rather than protecting Dr. Venture, Brock and his predecessors were there to prevent the activation of an ancient and presumably dangerous artifact. Agents were informed to watch out for the patch of land the instructions to find the orb were hidden upon assignment to the op. If necessary, termination of Dr. Venture was actively encouraged. In The Revenge Society, it is discovered that when Col. Lloyd Venture decided to activate the Orb, his bodyguard, Eugene Sandow, tore it in two instead of killing Col. Venture. Col. Venture was upset until Sandow told him his orders were to kill him. Col. Venture then decided that it was okay and they should keep its state of disrepair a secret.