After that, its more or less whom is the most powerfull. I like to match my civ against theirs just for the sake of killing off the contenders to my title.

I dont' mind weak civs becoming powerfull after another world power has fallen to my mighty armies. Rarely are they going to be powerfull enough to give me any real problem.

Like many other folks on this thread, I tend to terminate my nearest neighbors when the opportunity presents itself.

Unfortunately, I happen to also be a "builder" type of player ... so more often than not, I end up having to bully my way through a half-dozen or more AI cities before closing in on the last, desperate outpost of an enemy nation. Most of my nation-destroying comes after I've acquired gunpowder, cannons/artillery and calvary. It only increases with the advent of armor, flight and assorted other technologically murderous goods.

On more than one occasion I've encountered monstrously-large empires built/conquered by Mongolia, Russia, Zulus and other aggressive AI civs. Those are babies I tend to crack only when I've got eight or nine transports loaded to the gills with armor and howitzers, along with air and naval support. Guess that's what I deserve for being a "builder."

BTW, the Indians are fun to toy with. It's easy to piss them off early (say, first contact).

The rest were never really much of a challange. This is of course only on the world map with not random starting spots, (Although I don't think Civ 1 had that option), the monguls and indians could sometimes get big but not normally.

In Civ 2....who ever I meet first is usually the first to go. I usually try to pick on the largest Civ, if it's not me. The worst thing you can do is kill all the smaller civs and then have one HUGE one left and your screwed. In 1900 sending your tanks in triemes because you have no money or production!!! Anyway.

The main question I ask is "What do I gain by eliminating the civilization?"

Reasons for going to war with a civ are, in order of importance:

Take out anyone on your continent, then either the next closest or the biggest threat either way.

If my opponent calls himself the "Bloodthirsty Pirates"
or calls his cities "Hell" or "Death Awaits-U"; I assume the worst of their intentions and believe it
most appropriate to get my retaliation in first and capture, destroy, pillage, steal at first opportunity.

If he/she call cities 'Peace', 'Harmony' etc; I inevitably make peace and will even send caravans.

If he renames cities to "Edward is Excellent"; I may even give him 50 gold for fortitude in arse licking.