Oh, yeah, about the Medic promotion. I usually have a Spearman early on that takes Medic, or, when I fight with Cavalry one of them also gets Medic since sometimes I'll use them to move deeper into enemy territory without support from other troops. And I'd rather have an extra unit that can fight then a Medic-only one, so that's why I never build Explorers.
As for Bombers, Fighters, Stealth Bombers and Jet Fighters they are excellent to replace your Artillery, as OceansEleven said. I also use them to scout an area before attacking if I don't have Open Borders or Spies. For this purpose the Stealth Bomber is just the best, as I can usually map nearly all of my enemy's territory with 4-5 of them in the same turn. Unit distribution, defenses, lines of attack, everything can be updated in an instant.
I did also find use for Carriers. In a three continent map I started a war with an AI who had two coastal cities on a small distant continent. Rather than shipping a lot of troops there I got a few destroyers, two battleships, just in case, no less then four carriers full of jet fighters and four transports full of marines. The sea counter was pitifull, so my ships bombarded the city defenses while the fighters reduced the life of the units inside. My marines stayed safely loaded in the transports until the city defenses were down to 0, and all troops were at half-life, then I took the cities easy as pie.
Anyway, I bet that on maps with a lot of water you'll find carriers very usefull for late wars, as most of the time you won't be able to base your fighters or bombers on a city on the island you want to attack. And sea attacks have the advantage of not allowing a counter-attack against the transported troops, so a destroyer-carrier-transport-marine combo can prove to be quite a force.