I rarely build much of a navy before Ironclads. The rule for Ironclads is simple... every coastal city builds at least one, immediately upon Steam Engine. With SunTzu's and Magellans, they rule the world. The only thing to watch out for is Leonardo's upgrading them to destroyer, which will remove the critical Veteran bounus until it can be regained. Diety, large map... about 30-35 Ironclads, minimum, are in order.
Battleships and AEGIS Cruisers (always vet) rule the seas. No AI navy is allowed to exist in any location I desire.... Transports are essential to getting those freight with 2,000 and 3,000 gold bonuses through on a regular basis to the biggest and best enemy cities. Shortly after coprporation, I expect an advance every turn, even in Fundamentalism. And a Strong navy will allow a steady 3,000 to 5,000 gold and science every turn with Freight.
AI cruise missiles are a joke, if you have multiple vet AEGIS to protect the stack. Vet Battleships can be taken out with as few as 2 lucky cruise missiles, however.
Carriers are excellent for ferrying fighters and patrolling large ocean gaps. I have never built a stealth bomber. Stealth fighters, spies, howitzers, engineers, and frieght rule the world at that point in the game. Bombers are an utter and categorical waste of resources in all circumstances at diety level, esp. if fighting in a democracy with a huge army and navy (which I almost always do).
That said, it is possible to win with a weak navy or even no navy at all, but it will generally be slower, lower scoring, and economically weaker, depending on difficulty level and map characteristics.
[This message has been edited by starlifter (edited June 18, 2001).]
[This message has been edited by starlifter (edited June 18, 2001).]