I love marines! Here are a few nifty tricks.
1. Slaves! - load two marines into a transport. At the start of a war, bombard the improvements in a key coastal square away from the front. When the AI sends in workers to repair the damage, send your marines on a suicide mission to capture them. You'll lose the marine, but you'll be able to capture the workers. Do this enough, and you'll completely cripple the AI's ability to recover when it comes time to bomb it back to the stone age.
2. Blitz! - The most common tactic for amphibious assaults involves 2-stages- first, land your forces with ton of defensive units on a mountain or hllside, beat off the initial counterattack, then take the city on the next turn. The problem is that you need to find adjacent to a hill-mountain, which limits which cities to mount your initial assault. Marines give you greater flexibility, and let you take the city on the first turn. Two transports - 16 marines - are enough to take one city defended by infantry if you lead with air/naval bombardment. You can then land your defensive troops at port, letting you fortify them and increase your chances of holding against the inevitable counterattack. And since any coastal city will do, you can be selective as to where to begin your attack. I like to land with 16 Marines, 12 Infantry, 4 Tanks, 8 artillery - far fewer units than I'm comfortable with on a 2-turn landing. If we're in the modern era, I just add an extra transport full of Marines.
3. Oil! - The AI defends its cities well, but not equally well. Small cities tend to have only 3-4 defensive units. Where do you find small cities? On desert and tundra squares, which happens to be where you also find oil. Two transports are guaranteed take out a city fortified with infantry, three if they've got MI. Take out a strategic resource in a single round.