I play Monarch and above (Although I have a poor win rate at Diety).
I find that I am am able to absolutely devestate any enemy with Bombers or SBombers on carriers. I generally skip all Sea power after galleys until Destroyers and then Carrier/Battleships become available.
I will develop flight, stockpile Bombers while researching for Carriers and then everybody had better watch out.
Except for Diety level (where I still can't ramp up my production to match the AI), I normally produce 3 to 8 Carriers loaded with ALL bombers and also 2 Battleship/2 Destroyer/1 Sub protection. A fleet of this size is only vulnerable to Nukes which come much later. Cruise missels and Artillery are avoided by moving my Carriers in to the shoreline, bombing, and then moving back out of range.
Normally, I do not use fighters for protection, I just keep building bombers and replace on the Carriers as necessary.
I concentrate on - IN ORDER - 1) Military Impact Resources - Oil, Coal, Aluminum, Uranium, etc. 2) Luxury resources. 3) Road systems to cut off individual cities. 3) High cost or multiple move replacement - Anything on a mountain, then Jungle or hills. 4) Cities - Destroy the Harbor!, Destroy the Airfield!, LOWER the Population to prepare to TAKE the city.
I also find it very helpfull to bomb 3 squares wide completely around a city until every improvement is gone. This prevents any ground forces from reaching the city if I have just taken it and it makes the city almost useless to the AI while we are still at war.
Lastly, the 3 square swath of totally bombed out squares is also great for isolating entire sections of enemy land, It will require any ground forces to move a second time to cross the swath and slow him down. I ALWAYS try to do this before I land troops (and 1 Settler).