For Monarch and above, however, it's well accepted that you pretty much need an ancient era war to wipe out and capture the cities of two or so close opponents to have a chance against the AI bonuses.
Accepted by whom?
Perhaps on Deity, this is necessary. I don't know, haven't gone there yet, don't really plan to at the moment. The rabidity of AI expansion is annoying enough, and the enemy civs are competent at Emperor level. Yes, I'm back to emperor already, after one half-game at Monarch post-patch yielded complete, utter, and hopeless domination (sans war) by the end of the ancient era. I had a great start, but it was more than that, so back up to Emperor I have gone.
With this new patch, the ancient era conquest idea has taken a serious hit. Cities with no culture are autorazed, tanking the "following the warrior-settler pairs and take over the new cities" strat forwarded by randomturn. To win cities by conquest, you must now attack the heart of an enemy empire, and that's no mean feat in the ancient era. To be successful at that, you have to focus on it, which means you don't have time to expand through "normal means".
I have two STRONG wins on Emperor with no ancient era war, so forget that "must do" portion of the concept. It may still be desirable, but let's not take it for granted. Some may depend on your civ choice, too. If you opt for a civ built for middle age or later dominance, with it's Unique Units, the ancient era may not appeal to you as a conquest phase.
Charis: for comments specifically about "what's new vs Civ 2" I refer you to my Civ III page, to the account of my first game. I went into some detail about all the mistakes I made, especially those regarding misperceptions left over from previous renditions.
Sirian's Great Library
The prevailing wisdom is generally strong, but it's not infallible. I've learned some things reading what others have had to say, but only lately, as I purposely isolated myself to play and discover on my own for the first month. The game purposely allows for any civ who falls behind in tech to catch up easily, and makes taking and holding a tech lead difficult. The patch seems to have magnified this factor. I am still evaluating that. But the bottom line is, if you engage in rabid expansionism of your own, you can compete at Emperor if you forego early wonders and concentrate on expansion. No matter how far you think you fall behind, if you have land comparable to the AI's, you can catch up, as human intelligence guiding workers and production and city placement and what squares within cities to use from turn to turn makes ground on the AI's bonuses over time. War is the other option, but I have a feeling that that is mostly due to loopholes, some of which have already been closed, others will be closed in upcoming patches. Or... I could be wrong, but I do get the sense that THIS design team cares about game balance. You know? And judging by their first patch, they are actually competent at it. Ancient wars are going to be less dominant once the design flaws are worked out.
There are more differences from Civ2 than are apparent at first. I found that out the hard way. Feel free to benefit from my mistakes.
It's all laid out...