Just my two cents worth....
1) The first tanks fielded during WWI were absolutely horrid. The were in effect moving pill boxes that could be easily stopped and blinded. Even the more modern tank of WWII had limitations against foot soldiers. The person in control of the tank has to be able to see. Fire was effective against those atnks for several reasons. They had no air conditioning, they were extremely hot and uncomfortable to operate. Open flames is a bad addition to this. The fire also consumes the limited oxygen that could make its way into the tank. Also the driver and commander had to look through slits to be able to see. These were not modern optics but holes in the armour. If the tank is burning, you can't see what is going on and you are a sitting duck to have your treads taken out. Once a tank was forced to button up and close the view slits it was useless. Tanks are good in a limit amount of terrian and weather conditions. During both wars, tanks assualts ground to a complete halt during heavy rains. Also, if tanks were so great at amphibous landings (like you can do in CivIII) why didn't we use them in the Pacific theater like we did in Europe. They were useless in the terrain and conditions of the pacific. Also, tanks had to stop to aim and fire effectively and as mentioned above a stopped tank is a lot more easily incapicitated.
2) I recall an engagement during WWII were a town of untrained civilians took a company of tanks, without anti-tank weapons. They allowed the tank to enter the city and chase them into narrow citty streets. Once a group of tanks was in a road were they could no turn, the people jammed the treads with large fence posts and rocks. The turrets couldn't turn to confront ther attackers (and it does no good on an attacker already at the tank). Stopping a tank at the front and rear of the column stopped them all. Then they only had to wait for the tanks to surrender. As mentioned above you couldn't stay in the tanks for really extended times.
3) Afghanistan....saw a article were the Northern Alliance on horse back was kicking some tank butt beacuse the terrain was not suited for the tanks. Mobility was in the horses favor.
Modern tanks have gotten rid of a lot of the limitations (air conditioning and control, modern optics, compensation for aim while moving). An example between current tanks and WWII tanks would be the limited action between the M-1 Abrams and the Soviet T-55(6) seen during the Iraq conflict. The older tank were far outclassed by the newer versions. I saw footage of M-1s literal making passes at speed through the older tasnks (as they could move and shoot) will the older tanks could not even turn their turrets fast enough to keep up.
Just because the unit says it is a tank doesn't mean it is a good tank, or that it was all of the video combat tank bells and whistles. Tanks have always lost and will continue to lose to suprior tactics and (on the suface) worse units. It is acually getting worse for the tanks. We have probably seen the last of the great tanks battles. Air superiority wins ever time. You can't run and you can't hide. Something not really shown in CivIII as it would totally unbalance the game play.
Given a year or more to fight and the proper tactics (like attrition, cut off of supplies, harrasment) A lowly spear unit can and should be able to take out those tanks. With proper support and combined arm it tank should have an easy time.
Give me mountians and snipers and I will take on that tank battalion. Any day.