I play one city challenge, two, five, etc... I find them much more enjoyable because they limit the expansion phase of the game which can otherwise become very tedious, and they force you to interact diplomatically to get resources and such. Resources are probably the biggest challenge. If you're smart militarily, you can use artillery and forts to destroy a much larger enemy force without too much trouble, but it's difficult to keep your military modern if you don't have saltpeter, oil, aluminum, etc...
And of course people probably play with varying degrees of strictness. I don't enforce the 5 city limit as much as others. I know some people only raze cities they take so they never have more than 5. I tend to gift the cities to other civs (not the civ I took it from) because razing would kill my reputation.
Also building colonies actually becomes important.. either for resources just outside your cultural reach, or more frequently resources on some island that the AI has a city on. Build a colony, connect by road to their city, and make sure you're at peace with them
Playing on archipelagio makes it much easier, as well. You can find good chokeholds to defend, and won't have too many neighbors on your continent (if any). The big problem with archipeligio is that you rarely find rivers, and rivers are huge for your capital- all the extra commerce makes your science considerably better.
The relative values of wonders changes a lot, as well. All of the wonders that distribute effects over all of your cities aren't quite so important any more. The colosus, science doubling wonders, and shakespear's theatre are HUGE. Also the unit generator wonders (zeus and knights templar) can be more helpful than they normally would.
On a small map, 5cc is really not that much harder than a normal set up. You don't get a Forbidden palace or as many armies as you'd like, but you can build the small wonders that rely on 5 of something. 2cc is significantly harder, and 1cc is much harder still. A second city is huge to be able to produce military while your main city works on wonders, or to produce workers, or to expand your resource grasp. You see diminishing returns the more cities you add.
cultural 20k is the easiest victory. Diplomatic can also be fairly easy. Space race is possible as well (though you almost need to disable cultural victory to do it).
The way these games play out is that you're always fighting hard to stay ahead in the tech race. You can export luxuries (they aren't that important to your cities, often) for gpt, or trade older techs for gpt, and try to stay at 100% science.
