I always leave it on. I'd like to see some subtle tweaks to the culture model, but mostly I don't mind it. I'm so grateful for national borders that I'll forgive the occasional silly flip.
What I'd like to see in Civ 4 is "allegience" precede the flip. So maybe the result of "flip" would be more likely than it is now, but the effect would be that a single citizen in that city would change to your nationality (while staying in the same city). The only way a city could truly flip would be if it had at least one citizen of the nationality it wanted to flip to. And as the percentage of such citizens went up, the chances of a full flip would likewise increase.
This would mean that you'd have some warning. If you had a unhappy city near the front that gradually switched "allegience" to a neighbor and then finally flipped--well, you deserve it.
Now by itself that wouldn't help the military problem at all. (Make it worse, actually). But I'd also like to see "immigration". If a CIV had a big culture lead as a whole civilization OR if nearby cities were much happier across the border--then some of these "allegience" switchers would flee across the border to a nearby city of their choice (that had room to grow). When a city falls to an invader, a lot of the citizens would have a high chance to suddenly "immigrate", since these refugees would naturally flee. *That* is why a just conquered city wouldn't flip so easily. The population would be relatively low because a lot of the citizens with initiative would flee before you got the city.
As a nice side effect, players with qualms about starving the population of captured cities could avoid that. (And if you tried to starve a city that was still fairly large even after capture, the unhappy citizens would quickly "immigrate" before they all starved.) On the other hand, if you are losing a war, precious citizens will flee back to your homeland until your cities are packed.
If you aren't prepared for the growth, these refugees might cause unhappiness problems. Or they might provide the extra production you need to turn the tide. As a dying CIV gets more compacted, flips become more likely because the refugees have nowhere to go. This favors shorter wars instead of extermination. If you overrun a CIV quickly, and it is surrounded by other CIVs, a certain amount of the population will "immigrate" to those other CIVs.
Finally, this would make growth slightly less important and culture slightly more so. I keep seeing the expert harp on how "population equals power." Well, this would provide another way to get that population. Strategic choices are good.