Bought the game last week Friday, played as Spain and finished the game by Monday (on Medium/Medium). Second game now as Egypt on hard/hard.
Some notes on things I noticed:
Concerning the pope:When the pope tells you too stop attacking someone - do so!
If the AI attacks - let them, defend and quite quickly the enemy will be excomunicated (you can always strengthen your army, or rather - disband lots of your army - get money in, and one or two rounds before the papal order runs out, rebiuld your army) at which point you can attack them without being punished.
Do NOT attack the papal states. Once at war with them you obviously are immediately excommunicated (giving you a 20% unrest increase in all cities - which is a lot with a larger empire). Even conquering Rome and killing the pope does not help - a new pope is elected, but as long as you are at war with the papal states (who can not be eradicated) you will STAY excommunicated, no matter who the pope comes from.
Which brings me to the next point - training of troops.
I LOVE that you can train several troops per round (and all troops only take one round to train!). This makes it possible to disband most of your army (leave one unit per city) during peacetime, so you get lots of money, build up your cities, and as soon as someone declares war, you can train a large army in one or two rounds.
Merchants: Either completely ignore them, or always build to the maximum. Then send them all to the same kind of resource (for example wine), so that you have a monopoly - which gets you a good bonus. I had a monopoly on wine which gave me between 30 and 60 gold per round per merchant (changing my capital to Rome had me suddenly make several hundred with some other merchants, but changing to another city and then back to Rome had that go down to 50-70 again :/.
Driving enemy merchants out of business depends on your merchants finance trait - so have some good merchants to kill all of the enemy's merchants.
Spies: ALWAYS build as many spies as possible - You need at least one spy in each of your cities relatively close to the front (to detect enemy spies). Placing spies in enemy cities of course gives a chance that the gates are open when you attack. Very useful: Spies increase the unrest in the cities they are in - several spies in one enemy city far from his capital can quickly cause them to rebel. Important: Every round move the spies out of the enemy cities and in again (when probability of success = 100%) and into the city again (increases the spies traits).
For cities: You can have cities (towns) or castles (fortresses) - Cities give more money, fortresses better troops (better infantry, cavalry, better archers, siege weapons). I usually have only one fortress, and the rest as cities (more money = more troops, which trumps less but better troops). Once gunpowder is invented you can build cannons also in cities, which reduces the need of fortresses. Additionally, built up cities also have cavalry.
For armies (and battles):
Siege weapons (especially Trebuchets and of course all cannons) are EXTREMELY effective. Not only in killing enemy troops, but especially killing their morale (especially Trebuchets with their cow cadavers you can toss, which infect enemy troops - and even spreads to those you didn't hit! - which greatly reduces their morale).
Archers: You need LOTS of archers. I usually havehalf my army as archers. The AI is hesitant to simply charge your troops, and instead first tries to attack you with his archers (which he always has less of than you, except mongols), which enables you too kill or demoralise most of his army by the time he charges.
Cavalry: You need at least two cavalry units to swing around the enemy and attack from behind to get the enemy fleeing.
Note: You goal is not necessarily to kill the enemy army, but to get his army to start fleeing, at which point the real massacre begins. So always set up your army and tactics to get the enemy to start fleeing (not possible against mongols, which is why they are hard to defeat).
During Sieges:
When defending: My experience is, that it is better NOT to defend directly at the gate (like MKSheppard shows in his screenshots), but instead retreat into the city a bit, and place your engage the enemy in the streets - this causes his units to be spread out and fight ineffectively.
When attacking (pre gunpowder): Stay out of the "no-routing-zone" - the city square - as long as possible. Once in it you usually have (comparatively) - massive losses.
When attacking (with cannons or bombards): Have at least 5 or 6 cannon units. As soon as the battle starts, blast the enemy walls to bit that are defended by units - you can usually kill 50-100 soldiers at once (playing with huge armies) per wall - anything less than the biggest walls are almost immediately destroyed by 3 artillery units shooting at them. After that, start demolishing the towers. Then the long part comes - start manouvering your siege weapons so that you can get clear shots (through the destroyed walls) at the enemy killing as much as possible with them before attacking with your normal units.
Altogether, as Spain it was very easy, overran most of western Europe, erected some nice crusader states in Israel, and was finished quite quickly.
Second game, which I'm still at, I'm playing as Egypt (on hard/hard). I wanted to try not to go to war with Europe so I didn't attack them (only conquered the orthodox Byzantines

), sent diplomats to everyone made alliances, gave them presents (maps only

)and was very nice to them.
So what happens?
CRUSADE!!! Argh. (against Jerusalem my new capital)
So I build up troops, posted spies in enemy lands to watch for the crusaders. The Hungarians came first, with a full stack of good troops.
He boarded some ships in order to reach the Holy land quickly - which was the dumbest thing he could have done. I had several fleets patrolling the eastern Mediteranean all the way to Italy, and of course also the Black Sea. Needless to say his fleet didn't survive a single round, and his full stack army went down with the waves (and my reputation with all of catholic Europe went down too).
After that, the Turks broke their alliance with me, the first warning of the approaching Mongol hordes had come - and I still had Jerusalem as the goal of the Crusades. Finally, all the different diplomats came to me, I signed peace treaties with all parties concerned, started pulling away my army to attack the Turks and the soon to come Mongols. Suddenly, out of nowhere (those crusader armies are FAST) TWO enemy crusades attack me.
Bastards.
Turn around all the troops, train new ones, etc etc but drove them off too.
And the crusade was called of. Yay!
So I start attacking the Turks, and the Mongol hordes arrived two round or so later (directly in the Turkish heartlands - hah! - which I wanted to conquer - doh!).
At this time I start mass producing troops - mainly archers and spearbearers. I have not stopped producing troops since then (around 20 rounds or so later). I am currently paying "only" about 55.000 or so per turn for my army, as I had a small reprieve before the second Mongol Horder came.
The Mongol hordes are fucking crazy. The first horde to arrive consisted of about 6-7 full stacks of armies (50% cavalry archers, 30% archers, 20% light of heavy cavalry - ALL of them with 6-9 or so experience, each stack lead by a 6-10 star general!!!).
I have almost never been able to cause a single unit to flee - only when 120 archers of his get attacked by 1500 of mine, and even then only when they are down to 5-10 men!!!
I have just recetly been able to disperse most of this 6 stack army, so now the next horde (of only 4 stacks...) has arrived.
When defending against the Mongols (note: His generals can always attack at night, so you need good generals yourself, or each of your armies has to fight on their own.: LOTS (70%) of archers, some spearbearers (20%) and the rest cavalry (the first cannon units have also started arriving). Let the Mongols attack you (stay in the mountains)look for some tiny corner high on the mountain which is hard to reach, and then let them come (Screenshots will follow). This way you can kill the enemy army while (under optimal conditions) only losing 20% of yours.
The problem is, that this situation is rare
When attacking a Mongol army, it is a long and tedious affair - they avoid your army most of the time, and when you extend yourself a bit too far, they charge you immediately to death. Or if you want the computer to duke it out, you need 3 or so stacks for each of his.
All in all I love the games, though certain aspects grate (still no sea battles, and some other things mentioned by others).
Screenshots:
Defending in the city, and not at the walls.

Victory! Most of those losses were pushing the enemy back to the gates - I would have lost less only defending at that courtyard.

A great battle: The enemy is on the mountain and I can't reach him - I had to reatreat, which DISSOLVED the army - WTF?!?!

Killing one Mongol stack. Note the small entrance

The dead Mongol stack - note one of my units fled after having about 20% losses -WTF

The second Mongol army approaching - its AI acted as if I were the attacking army and it the defending one - I had to go out and be slaughtered... stupid no-limit no-limit-timer...
