I love Tanks. 
And while I know that the diehard warmongers would consider a game that lasts long enough to see them a disgrace, I’d still like to share some thoughts about how to make the most of these lovely, rolling implements of destruction. Experienced warmongers may view much of this as obvious implications of the combat system, but hopefully there will be a few tips useful for everyone.
Significance: The combination of two moves, collateral damage, and city raider allow one to capture enemy cities far more quickly than in previous eras. Conquering a city every other turn with only a modest battlegroup (i.e. 10-12 tanks) is easily possible, given the right tactics. This can have tremendous impact, whether you’re a builder looking to demolish a rival or a warmonger looking for an early end date.
Objective: Conquer enemy cities as quickly as possible. At this stage of the game, IMO, losing an occasional tank is well worth cutting your conquest time by 50%-75%. The war weariness, supply costs, and wasted turns before victory are more important than a few hundred hammers. If you are significantly behind your enemy and are trying for a desperate late game power-grab, these tactics may not be appropriate.
Assumptions:
1) You are at least close to tech/power parity with your victim. It’s fine if he has gunships and/or SAM’s. If he’s far enough ahead to already have Jets or MechInfs, then you’re probably too late.
2) You have Flight and Radio (for Fighters and Bombers). Having Rocketry (for Gunships) and Robotics (for MechInfs) is nice, but by no means required. You also need Airports in your major military production cities.
3) You have a reasonable supply of Level 4 (10XP) units. Just having a military city with West Point is enough – you don’t need a ton of Level 4 units. Having the Pentagon and civics such that every city can produce 10XP troops is obviously nice, but again not strictly necessary.
4) You’re playing on Settler. Kidding… this works fine at least through Emperor, provided you can stay in the game well enough to meet the other criteria.
What you need:
Tanks: Well, duh. More specifically, you need several kinds:
1) Raider Tanks – your heavy hitters: You want 3 of these, 4 is better. These are the ones that really need to be Level 4 to be effective. Take Raider I, Raider II, and Barrage I promotions. Take Raider III at Level 5 if you get there.
2) Drill Tanks – cleanup crew: How many you need depends on how many troops you’re up against. A number equal to the number of defending troops is safe. If you’re in a time/production bind, you can reasonably count on blitzing for multiple attacks but make sure that the target city isn’t on a hill (costs 2 moves to attack). Promote these with as many Drill promos as you can get.
3) Cover Tanks – protection: You want 2-3 of these, depending on how much you fear the enemy’s counterattack. Promote either all Combat or Combat I/II, Ambush depending on whether you think a counterattack will be heavier on tanks or artillery/gunships. If you have Gunships, one of them can replace one of these. If you have MechInfs, use them instead. On the very first assault of a war, these will take a larger beating as the AI throws its extra troops at them. For the fastest conquest, keep two extras safe behind your lines and ready to move.
Non-Tank units:
1) Medics – Explorers are essential for this, because they’ll likely be the only available 2 move unit that can take medic. You need two of them.
2) Bombers – The more the merrier, but 10 is probably enough. 15 can cut through even the toughest air defenses I’ve seen. More than that is overkill. Expect to lose about one for every other city and be ready to replace them.
3) Fighters – Two or three flying Interception within range of the target city. Only needed if the victim has Bombers himself, in order to intercept bombing runs against your approaching stack.
4) Worker pair w/cover – Very important. You need to be able to quickly build rails in conquered territory. In contrast to Civ3, the AI doesn’t appear to be very keen on snagging covered workers. I tend to cover with only a single tough defender like a Combat I/II/Ambush Infantry. An extra cover unit would be safer. Having two pairs of workers is also nice, but not essential.
How it works:
In most situations, this will be a two turn process – one to approach and the other to attack. If terrain, culture, or a reliance on blitz necessitate an extra approach turn, you may want to hold off some or all of the bombers until turn two.
Turn 1:
1) Tank group approaches. Since tanks don’t receive terrain bonuses, you generally just want the fastest path. But sometimes you can position yourself so that incoming attacks are across a river, which is helpful.
2) First bombing run – balance is key here. It’s important to damage the units in the target city on this turn since the combat system significantly penalizes weakened attackers. You want counterattacking tanks, artillery, and gunships to come at you at no more than 75% strength or so. At the same time, your airstrikes won’t be effective until you’ve lowered the culture defense, and of course you need to start softening them up for your approaching tanks anyway. Keep in mind that, at 15%/turn, it takes 7 successful bombing runs to completely eliminate enemy defenses. I tend to go about 60/40 %bombard vs. unit bombard on this turn. %bombard first, then unit bombard. If you have a surplus of air power, it’s worth looking around at other cities near your target in order to weaken any responders there.
Turn 2:
1) Second bombing run – Finish what the first one started. You should really have enough bombers to both zero out the cultural defense and reduce all defenders to 50%. If that’s impossible, go for a balanced approach. If the enemy has bunkers (which is pretty rare, in my experience), try to make sure that every unit takes a few hits but don’t get hung up on it.
2) Raiders attack – This wave has two objectives – take out the toughest defenders and soften up the remainder for your drill tanks. These tanks will take damage, though hopefully not be destroyed. Do not use every raider tank you brought. Two is enough – the goal is speed, and the more damage you suffer the more time you spend healing. After two collateral damage hits from these the rest of the defenders should be under 50% strength, and it’s time to move on. The third/fourth raider tanks are purely for backup purposes in case the other two get badly beat up by counterstrikes.
3) Drill tanks attack – This wave takes advantage of first strikes, letting your drill tanks sweep up defenders with a good probability of taking no damage. Nothing elaborate, just send them in. Don’t blitz with a wounded tank unless absolutely required – not because you’ll lose it, but because you want to minimize healing time. This wave should capture the city. If you’ve never tried this, expect to be surprised at how your tanks can go 5 for 5 battles or more without taking a scratch.
4) Move in to the city? – This gets tricky, depending on how the enemy countered your advance. If you have damaged tanks (from an artillery or air strike, perhaps) that haven’t moved, you may want to leave them outside the city to get an extra turn of healing. Just make sure they’re protected by one of your cover units, and keep one of the medics there of course. The AI doesn’t seem terribly interested in picking off your stack provided that it’s covered. Otherwise, move them in.
5) Fly in a garrison – You do have a garrison infantry waiting at a friendly airport, right? Your shiny new city can accept one airlifted unit each turn, even while it’s revolting. Make sure you have another one for next turn, too. If you want a larger garrison, you can airlift to the nearest city and move it over via rails.
The result:
You have a new city and a bunch of tanks that need, at most, a single skipped turn to heal. After you’ve weathered the initial counterstrikes in a war, it’s entirely common that only your lead raider tank takes any damage at all – let that one stay behind to heal up, and the others can start their next approach on the turn after the first assault. Typical losses are 1-2 tanks and 3-4 bombers for a sustained campaign taking 6-8 cities from an enemy of roughly equal power. If your unfortunate victim doesn’t have any far-flung island cities, a tank campaign along these lines can eliminate an enemy civ in under 20 turns.
I think that’s pretty much it. I hope these tactics prove useful in your conquests. Comments, questions, and improvements are welcomed.