What do you think: is a R/C car a robot? It moves, however I think many people would say it is not a robot. What then are the mars robot explorers other then glorified R/C cars with cameras, other attachments, and a longer range radio signal? Perhaps it's the recreation aspect? However, the robots competing in battle bots were for entertainment, as well as being remote controlled, but they qualify as robots (don't they?). So it is not the remote control aspect either. Maybe we should start at the other end of the spectrum.
A fully humanoid automated mechanical being would obviously be considered a robot (ie: C3P0 from Star Wars). Today industrial robots are most commonly the robotic arms that weld, rivet, and otherwise work on mass production assembly lines. That common definition is not what most roboticists think of when someone says robot. I think we can be safe in saying that robot must contain some kind of electrial components (yes mechanical ones might exist but I doubt they'd hit the level of robot-hood, more likely they are automaton). What else, must a computer contain to be a robot?
How about a large Dancing Santa , is that a Santa robot? I think sensors are another important component to robots. These dancing Santas wouldn't qualify because they merely have an on/off switch. Before you ask: NO! Dancing sunflowers don't count just because they perceive sound. Let's modify that definition to include sensors to perceive with AND some sort of complex processing of that input. That eliminates remote controlled robots.
But are those remote controlled robots really robots in the strictest sense? I don't believe so. I'd have to say they were remote controlled devices. And the debate continues……
Current definition of Robot: Moves, has electrical parts, has sensors and processes the input received from those sensors.