I haven't yet reached an endgame in Civ IV that has been tediously boring. In fact, I had quite an exciting one a while back. I was the Germans and was on a pangaea, bordered by the Japanes to the east, and the Chinese and Mongols to the south. I had fought the Japanese in a war right around the Middle ages so I had peace with them because they weren't looking for another butt-kicking.
I had a comfy tech lead but the Chinese were gaining on me. They had a lot of room and had wiped out the Persians so they had a distinct population and city advantage on me. I began modernizing and expanding my army around the time infantry and tanks roll along, preparing for what I felt would be a showdown between Mao and me. Because the Chinese were becoming so strong, I couldn't bribe anyone to declare war on them to weaken them, nor could I get them to agree to help me in a war with them. I sent spies into Mao's territory and every single one of his cities had at least 10 modern units defending. Ouch.
I kept going with the military buildup, managed to get a few nukes built before the UN banned them, which meant I at least had a nuclear edge on everyone else. I began work on Apollo and resolved to win by spaceship while maintaining a large army as a deterrent. Well, about 5-10 turns before I finished Apollo, Mao built it before me. Time for panic.
I sent my spies in and his cities were cranking out casings and other spaceship parts. I set my cities to crank out parts, did a research crash program to get the parts I needed to launch before him, and massed my troops on the border for a possible blitz to derail his projects.
What resulted was a really cool cold war. Troops staring at each other across the border. Crash programs to send men to another planet. And spies. I sent out dozens of spies to destroy his casings, but this extremely expensive and drained my coffers quickly. I instead sent my spies out to destroy his access to aluminum and uranium. I destroyed roads and rails, demanded his allies stop trading with him. Anything to slow down his production. He caught my spies several times and was pissed but never launched an attack because of the size of my army on the border and his own preoccupation with constructing the spaceship. I had become wreckless in getting my ship off before him. And I succeeded. I launched about 5 turns before him and won. Down to the wire gunpoint excitement.