Alright, I want to present the case for building a Settler first.
FOR A NORMAL SPEED GAME ON STANDARD SIZED MAP
1.) Whereas the Worker/Warrior (or vice versa) strategy gives a faster boost in the beginning, a settler will typically provide more hammers/research over the long run of about the first 50-100 turns. I'm sure someone out there has done the math to confirm this, as I've seen the charts before, but unfortunately I just can't find them. In a nutshell, though, the rate of growth for 2 tiny cities will, within about 50 turns, outstrip the production of one city, one worker, and city tiles.
2.) If you build a worker first, (say 15 turns, avg), then grow your city (avg ~9 turns to get to Pop=2) while building a warrior, then build your settler (by that time, perhaps 17 turns), you have spent around 40 turns JUST to get your first settler out. This does not count travel time to your city's destination. Giving about 5 turns for variance and travel time, this leaves you at turn 45 to have one city at Pop 2 (maybe 3 at best), and one completely new city at pop 1.
If you build a settler first (25 turns average), and account for 5 turns worth of travel time, then by turn 30, you have 2 Cities at Pop 1. In 15 turns, both cities should be sitting at a pop 2 or 3, leaving you in a much better position by turn 45, with each city able to produce a worker in about 7 turns or so, and by turn 52, both cities are improving tiles and churning out whatever buildings/units you need.
3.) If you have a civ with an early UU that requires a special resource (like copper, iron, or horses), you can almost always reveal that resource in 25-30 turns, meaning the 2nd city you found can get you immediate access to your UU. Alternately, even if you have a late UU, being able to claim copper, horses, or iron (often in very limited number), or some other major strategic or luxury resource, can make or break the early game.
EXAMPLE: I played Darius of the Persians, (Immortals UU, requires horses). I started building a settler on turn one, left my cap unguarded while I used the scout to uncover as many tiles as possible in 25 turns. I set my research to Animal Husbandry, followed by roads. By turn 25, I've got roads, animal husbandry, and am only a few turns from finishing Horseback Riding. My searches have uncovered a horse resource about 10 spaces from my Capital, and my scout is able to meet my settler 2 spaces outside of my capital border. Scout escorts settler to horse while capital builds a worker. By the time my new city is founded, I've researched Horseback Riding and can start a warrior followed by a barracks. Once my capital finishes the worker, I use the scout to escort the worker from the capital to the horses next to the new city, where I develop the tile, place a road, and by then, I've nearly finished the stable. Meanwhile, my capital develops a warrior. About 20 turns later I've churned out 3 immortals with enough XP to give them a promo, and send them off to capture the capital of the Greeks, whom were unfortunate enough to be spotted by my scout when I was initially scoping the landscape. Within roughly 50 turns, I've founded two cities that are now at about pop=3 each, have started churning out UUs with xp, have taken over a size 5 capital city that has nicely developed tiles all around it, and I've just razed the last Greek City. My only competitor for space on the continent now gone, I can quickly escore settlers out with my immortals who can match their quick pace, and defend them from the barbarian warriors that are now roaming the countryside.
4.) Finally, most of us know by turn 50-100 if we're going to stick with the game or restart.