In my most recent game (Monarch/Standard/8civs, as usual), I got hit several times by AI civs, and each time the opponent had less chance of winning.
The first attack was by a civ that actually could have hurt me rather badly, had they massed their forces and upgraded propertly. Persia. With iron. Some solid cities.
I was the Greeks. So, to open the war, the Persians hit my border town (defended by a veteran hoplite) with a warrior. A single regular warrior. WHICH WON, suffering 1hp damage. I was, um, not amused. I destroyed them. It took a little while, but I wiped them out.
Later, I was sneak attacked by my former allies (against Persia), the Arabs. They were still pre-chivalry. I had Knights. They died, badly.
After that, I sent the majority of my forces overseas to pick on Carthage (relatively weak, had 2 luxury supplies controlable by coastal cities = target). That left America, the final civ on my continent, at my back.
Anyway, I beat the snot out of Carthage, and then settled down for a while. But then the Mongols wanted a piece of me. So, with what had to be over 30 ancient cavalry units, they came after me (they had no horses though, so no Keshiks). I slaughtered them with Cavalry, and ripped apart their empire with 3 4x Cavalry and 1 4x infantry armies.
And then, having toasted Mongolia, the Americans hit me. They had a very large number of knights, crusaders, guerrilas and infantry. I must admit, for several turns I couldn't actually repel them - I was just whittling away (except for that one border city I grabbed on turn 1 of the war). Had the attack come ~15 turns earlier, it would have been more problematic, because like I said, nearly my entire offensive army was overseas. But by the time the Amis hit me, I had just gotten Tanks. A few turns later, with 3 4x Tank armies leading the way, I had destroyed their invasion force, and started my counterinvasion.
That's as far as I've played.
The Persian attack: smart, but poorly executed. A proper Immortal rush might have wrecked me.
The Arab attack: suicidal. By this point I was numero uno, and they were the weakest civ in the game.
The Mongol attack: suicidal. Ancient cav versus Infantry and Cavalry, with armies.
The American attack: suicidal, but given the situation (I had the game won) understandable. Mistimed and poorly executed, though.
Fun, though.
-Arrian