If by "eyes" you mean the cameras or whatever sensors it uses to perceive the world visually, no. This is usually done in media for no better reason than because it looks cool.
In real life, many robots that are built for human entertainment have what seems like glowing eyes. But they don't see with those eyes. Take AIBO for an example:
At first glance it seems like the head lights are its eyes. Look again.
A robot could have glowing "eyes" so that a human talking to it will maintain proper eye contact, for whatever reasons the bot's designer had in mind -— in AIBO's case it can use its LED'sLEDs to communicate. Or they may work as flashlights (for humans, not for the robot) so that one can see which direction the bot is looking at even if they are behind the bot. Or they could serve as an indicator that the bot has your attention, or if it is turned on (i.e.: if the eyes are off, the robot is off or in stand-by).
Last but not least -— the robot may be secretly communicating using a protocol similar to morse code*code‡. They are blinking their eyes too fast for us to see. Think about it, a fluorescent light "blinks" 60 times per second and we can't see it. The robots have been telling jokes about us humans all this time right under our noses, next thing they are going to break the first law and kill us all.
*Yeah‡ Yeah, they could use radio to discuss their plans via bluetooth or wifi, but they knew we'd be snooping that kind of communication.