A Wikipedia entry states that only 1% of Internet data and voice traffic is transmitted through satellite links while the remaining 99% is still carried by undersea cables spread across the world’s oceans. This explains why Internet services get disrupted when these undersea cables are damaged due to passing ships or in the event of an undersea earthquake.
You should also check the recently updated Submarine Map which gives some good idea about the physical routes of these cables lying under the sea bed. This is an interactive map so you can zoom-in or click on any particular colored cable to know about their respective owners. Fascinating stuff.