They control their lifetimes. They can receive requests from external sources, such as other agents, but each individual agent decides whether or not to comply with external requests. Also, agents can decide to perform actions, such as travel across a network to a new computer, independent of any external request. By contrast, the Office Assistant in Microsoft Office is often called an agent, but it has only the limited ability to initiate offers of assistance within its own quite restricted environment. I actually admire the abstract artistry of the animated paper clip's contortions, and I find its natural-language help system much more effective than the typical approach that can only answer a question if the user knows exactly how to ask it.
Fiction is full of personified agents.
I am not a gadget, I am the state of the art. Likewise, more recently, the self-aware systems on Starship Andromeda. If you're looking for real-world agents, perhaps the most likely place to find them is on eBay. Real agents can't come soon enough for me. Off the Cuff appears Monday, Wednesday and Friday.