Playing King on huge Earth, Epic speed, victory types: max score only (time victory).
Depends on difficulty and victory types, i'd say 7-9 for tall empires on huge maps, however, not all built around same time. I have the feeling that map size also decreases unhappiness from population, and this kicks in substantially only when there are already some few 20+ cities - before that, it's not much a factor. So i start with 3-4 cities ASAP, grow 'em up, then fill gaps (if any) and expand by 3-5 more whenever i see happiness allowing it to be. Last game, by 1980s, got 8 cities each being 37...52 population each, most +happiness policies taken, - yet few still not taken, ~50 happiness reserve, so to say - and yet, standing at something like +70 happiness before conquest (temporary) penalties when razing cities. So i went on and made me two more cities in Carribean, for guaranteed naval passage from Atlantic to Pacific. Those two won't be properly tall, but could be.
Science penalty is at 5% on huge maps, iirc. So as long as your new city is able to increase total science output by more than 5% within a reasonably modest number of turns - which is doable, - getting another city is generally good (for extra gold, culture, strategic resources, more land control, you name it).
In my last game, my civ (Shoshone - no special things for science) is doing 3000+ beakers per turn. Which means if a new city is able to do 150+ beakers, then it's ok to get one. A city with size = 40 which is built near a mountain does something like 300 beakers, assuming all science buildings and specialists are present - i.e. twice more than needed. It is especially very nice if players can "buy" new cities - i mean, buy all the science and +food buildings right after making the city. This "launches" it to 30+ population in less than 100 turns on Epic speed, assuming at least some +food resources are present (as it should be), and there are at least a good bunch for 3+ food regular tiles. Domestic caravans can be used to reduce this "less than 100 turns" time dramatically - possibly to under 40 turns on Epic, if all player's caravans are put to it.
Note, you may want to have somewhat good (40+) happiness whenever you can, because on huge maps, some civs tend to build SO many cities that they get into huge -happiness, which causes some of their larger cities to revolt and, in case you maintain cultural lead, join you. Sometimes two at a time. Which can be quite a punch to your happiness - even if you put those cities into razing, it is still quite a few turns with a big happiness penalty.
And yes, i am doing lots of conquest. I don't puppet or annex even AI capitals with wonders, for a simple reason: whatever cities i need, i build - exactly where i want, when i want, and for whatever reasons i want, and on King difficulty, i am having _all_ the wonders i want to have (which is something like 80% of 'em). So, i have no reason to take that happiness penalty for annexing 'em. It happens i build a new city, - now and then, - very close to a location of a city i just razed. It also happens - alas very rarely, - when i happen to capture a city which is _exactly_ where i want one to be, and is large enough for its already existing population to worth more than happiness penalty - usually it's some capital. In which case, i decide to annex it and let it be. However, the later in the game, the faster it is to increase new city's population to some 15+ in something like ~30 or less turns (buying all +food + growth buildings at the city's day 1, of course).
Of course, i annex AI's capitals "technically" whenever i feel a desire to give those to some other AIs - but i gift those away during a same turn, so it is not "annexing" any much, if at all.
If you want to know, here's how it went in my last game (so far).
Razed all but one Inca cities, their capital - i captured and gave, right away, to Polinesians. Those two civs are only ones who don't have their own religion. Inca survived as a civ.
Then i took out Koreans, giving their Capital city to Inca. Left one medium Korean city to stay, but it was taken out by Indonesians.
Then i took out England, in the same manner. Capital to Inca, last city standing taken out by Indonesians again.
Then i took out Arabs, giving their capital to Inca as well. It was later captured by Dutch forces. Arabs survived with 1 island city.
Then i took out Polinesians, who survived having that Inca's capital as their only remaining city. Polinesian capital was given to Inca. Oh, the irony.
By 1980s, i am nearly done taking out Netherlands; out of their 30+ cities (those guys are insane, really), 5 are still around as a target practice until my pacific fleet arrives to Europe. Amsterdam is taken by a city-state ally of mine - took my time and made it by the book, even created detailed post about it today, too.
Two remaining civilizations in this game i do - Indonesians and Celts. The former will be dealt with just like i did the Dutch folks: i got ample time to arrange city-state capture of their capital, too. The latter - Celts, - i decided to spare my wrath, because they were nicely sitting in South America, are not a threat technology-wise and score-wise even if they'd have another thousand years - at 21st century pace - to develop, and because unlike most other civs, they are not bloodthirsty killers whenever they feel they have an easy target. Well, at least, less of that than most.
In general, i am completely dominating 'em all, being in vast lead scientifically ever since Koreans met their fate (for 100+ turns, they managed to be +-1 tech in compare to my science progress), having 4 naval groups (carrier with 5 jets + nuclear sub + missile cruiser + destroyer), two land-based groups (2 "terminator" bazookas + 1 GDR - each of those 6 units is level 10+; "paste" is indeed the right word), plus homeland-defense forces of some helicopters, mobile SAMs, a GDR and 3 bazookas. Whole game, nobody dared to attack me, though. Possibly because i keep myself prepared for it, hehe.
The Inca - despite all these capitals, - is still in Industrial age, as are few others; few others made it to Atomic age. Being crushed to a single city halts 'em real good, though. Polinesians, amazingly, managed to get a tech or two into Information age - but since i forced non-proliferation through the congress before they could build a nuke, it didn't help 'em none, since my conventional forces, trained by all those wars, are extremely deadly.
Last note. Try to keep piling up your faith; sooner or later, max Honor tree. Then you can get more GGs with faith. And you'll want more great generals - even with quite a bunch you'll be getting from regular warfare, - to get more resources for end-game war, which is Uranium and especially Alluminium. Burning a GG or even two to "reach" one more Alluminium or Uranium may be much desirable once you discover jet fighters (Alluminium) and GDRs (Uranium). Those 4 naval groups i wrote about above - that's alone 20 alluminium, i.e. 4 tiles with it. And to take out lower-tech civs, those birdies are extremely efficient. There were turns i was capturing 3 or even 4 cities per turn with all 4 carriers being all-out. Plus, any late-game expanding you may want could also need both of these resources - to build spaceship factory and nuclear power plant, correspondedly. For example, i have one Uranium tile being 10+ tiles away from one of my cities - took 3 citadels to get to it (and to one other tile which has Alluminium on it, too). And then, if you have any spare GGs, it's often possible to use 'em to create more convinient pathways for your forces around or through some other civ's territory (which you are not at war with, of course).
P.S. Oh, i lied. Previous note was not last - here's another one. Not directly related to your questions, but then, perhaps you'd want to know this: if, at some point, some other civ will propose to Embargo you - _agree_ with it in case you are 1st or 2nd scientifically. This removes huge +science bonuses AIs can get by trading with you. I just had self-embargo happily enacted by AIs with a bit of my ensuring "yes" votes in congress in my current game. No idea if chances for this are any dependant on earlier embargoes - in my case, i did embargo 2 highest (scientifically) AIs some time before. The thing is, you can't propose to embargo yourself yourself, so it might well be a one-time chance. Don't miss it. It relates to conquest very simply: the slower they are developing their science, the weakier units they'd be having at any given time - and scientific bonuses from trade routes can pile up quite substantially. In my game, there were too few cities any close to my territory at the time of this self-embargo being passed, - but still there was a trade route some AI made to one of my cities, and it was giving +13 beakers per turn to the AI. What if they'd settle up near you massively (before you'd take that particular civ out - or after it) and make some 10+ trade routes to you? That's 100+ beakers per turn to them. Significant, you see. As for where to send your own caravans - for me, not an issue; i prefer Freedom, which means i prefer to trade to city-states whenever possible, for that massive Influence boost to them. Having whole world of city-states being allies - is a good thing for conquest playing, too. They distract much of initially large AI armies. If captured by an AI (which is desirable), a city-state can always be "liberated" for that huge influence boost to the city-state. And then there are always domestic trading for extra food to whichever city needs growth, too. However, me, i never run short of city-states to trade with, even while i do not more than 1 caravan per 1 city-state (as far as i can tell, that influence bonus from Freedom - does not pile up from more than 1 caravan to a same city-state).
