I love the Rise of Rome, as Carthage (my favourite civ).
I learned a lot of lessons there, and I had to fight for every last tile...
When I started, I thought I was invincible- Rome was too far away to attack. I was naeive enough to build libraries... so when by chance, one galley dropped off a settler on a lucrative plot of land just outside Rome, I was surprised to find it annhilated by an army of about 20 Legionary Mk1 and 2s (about 10 of each). I had 2 War Elephants.
And so, I completely diverted my resources to war, the Romans marched, unstoppable into Spain, crushing my puny cities in their wake. Fortunately, my main cities survived, and Rome met its match- 15 Heavy Cavalry. Half the Roman army was destroyed on the first engagement, my cavalry retreated, 3 dead, all wounded to our closest city, then regened, and struck again. And again. Until the last legionaries were killed off in Southern Italy and my Cavalry paraded down Roma.
Then I invaded Macedon, expecting to find a navy half my size and a few Spartans, retreating wounded from the war in Persia. My Cavalry rode in, and found... Cavalry. Twice as many as me- we were anhilalated, their navy outnumbered us 5 to 1. In 2 turns, 10 galleys were built, they engaged the Macedonians off Sicily, won, then ferried across a full force of Cavalry, and after a deadly war lasting about 30 turns, the Macedonians fell.
The moral- you are only invincible if you know you're not.