Let me explain the circumstances behind this last attempt (which is still ongoing) as an example of how things are going.
QFT:
But more importantly, post some saves and/or screenshots and people will look at your game.
Since the game is ongoing, I figure there's no reason not to ...
I eliminated Caesar and now I am working on Victoria.
Why? What do you stand to gain from the war
you feel you need?
It sounds like you're well ahead of her and in a comfortable position to launch into space, so I'd bet the war was entirely unnecessary.
Alexander the Great is running in first place, his score is 2400 and I am at 1700.
Similar to above, unless Victoria has something vital to your Victory Condition (you should know it by now), Alexander is the only leader you should be worried about.
I think I may have kept a few too many English cities, because I start losing research.
Very possible. The only reason not to raze cities is if you hope to quickly vassalize your opponent.
Did you check to see if Victoria was willing to Capitulate? Vassalizing then gifting back the worthless cities is a great way to regain favour. (It's been a long time since I played Warlords ... could you gift cities for +diplo?)
I get attacked from across sea by Montezuma, which delays my offensive against Victoria.
Who is(are) Monty's friend(s)? (It's possible Victoria bribed him into attacking you.)
Before going to war, check diplomacy. If your target has close friends (especially warmongers like Monty or Shaka), try to bribe them to attack somebody else or somebody else to attack them. This keeps them off your back.
I fend off his attack (and I don't lose any cities), but I am falling behind on research again.
Similar to the above statement, if you bribe the whole world (especially and at least the top dogs) into war, there's less likelihood somebody will run away with the tech lead (since everybody's research suffers during the worldwide war).
What did I do wrong? Did I keep too many enemy cities? What is a good general rule...? When do you burn the city? When do you keep it?
See above comments.
General rule: If
{insert action here} doesn't directly increase your chances of achieving your desired victory condition, don't do it.
-- my 2
