I tend to play on a bit emptier maps - Try global highlands, standard, with the standard number of civs and you'll see what I mean. I usually end up adding more civs to the map, but even then there is still plenty of space if you move fast enough. As for number of cities, on a crowded map and lower difficulty levels I can usually grab at least 4 before I go to wipe out an opponent - and I always tend to play with aggressive AI and raging barbarians which usually leads to trying to build worker first or just spamming settlers with lots of wasted production and quick ends to the game. Without aggressive AI and raging barbs, it becomes significantly easier, but, also less fun IMO.
-Colin
Edit - there is also the matter of placement of cities. If I just go and place a city near my capital, and then expect to expand more sometimes I wouldn't be able to. But if instead I place my cities to cut off my opponents, and block off a section of land that I can then backfill, it is significantly easier to rapidly expand AND have somewhere to expand to. If the enemy is a significant distance away however, it is generally better to just choose the best available spot - but in that case you aren't in as big of a hurry to settle as you WILL have somewhere to settle.