Assuming we're talking Ethernet here - no, you can't use a passive splitter. But you can buy an Ethernet hub for $25 or less and use that.

I am using the connection to the Router to stream movies to my Home Theater system and want to enable another TV in another room. Are there any speed considerations I should be aware of to use an Ethernet hub? Is installing the hub near my Home Theater then connecting the hub to that system and then running another Cat5e to the new location OK?

The easiest, most reliable & consumer friendly way to attempt running streaming video to two separate media players (ie TV, Blu-ray, STB) at the same time is to use separate ports on your current router and run another Cat5e cable to your second media player.

Thanks, I was hoping there was a way where I did not have to fish another wire to the Router. I really appreciate your feedback and time.