Actually if the AI used the navy effectively most players would die swift deaths.
You can build a stack of destroyers, carriers and transports and take out coastal cities in a single turn without ever being seen. It's easy and only requires Vassalage and Drydocks (so you can pump out Navigation 1 Carriers and Transports and Combat 2 Destroyers).
Build enough Destroyers to bombard a cities defenses down to 0% in one turn. This would be about 7. Build a few more for protection, but usually the AI will be scared to attack a navy this large.
Build about two Transports per coastal city you wish to take. Most of your units inside should be attackers with city raider promotions. If you can get Marines early then GREAT, but it really isn't required to have amphibious. You WILL however be attacking exclusively from the transport. You should also plan to have 2-3 defenders per city. They will never attack, but rather just leave their ship once you take each city.
Build about 4-5 Carriers and 4 Fighters per Carrier. That's anywhere from 16-20 fighters. I like this many because if you don't bring enough then you'll never build anymore Carriers because they're annoying. Once you have all of the Civ's coastal cities you'll be glad you have the fighters because they can bombard defenses inland. Anywho, when you're taking the coastal cities you will be using the fighters for air strikes. If the cities aren't well defended you'll be able to take each unit down to 50% strength in one turn.
Most people are too afraid to attack from transports because of the 50% penalty, but if you bombard defenses to 0% and use air strikes you can take out a coastal city in 1 turn without any significant losses. Any loss you take is definitely balanced by not giving the AI a chance to nail you with artillary until you've already taken the city.
In other words, a navy is worth building. If the AI actually used their navy for anything other than pillaging your work boats then more people would build them.