Not sure if it's been mentioned here, but to address the not-completely-arbitrary-in-my-view choice by chess.com of an entry rating of 1200, here's what the USCF does:
Age = (Tournament End Date - Birth Date)/365.25
Initial Rating = 50 x Age, from Age 3 through 26; = 1300 otherwise.
If a player does not provide a Birth Date, but is inferred to be an adult, then Initial Rating is set to 1300.
Given that accurate birth dates are not available on chess.com and that a significant portion of new players are probably (my guess) less than 26 years of age, it seems reasonable enough to choose the value of 1200 as an initial rating for all incoming players. Using Glicko, a player's rating will move reasonably fast to a decent approximation of playing strength.
I would not find it unreasonable - though a good implementation would probably be somewhat problematic - to use federation ratings as an alternate initial rating, if one could be confirmed. Given the resource requirements for such confirmation, this is certainly not worthwhile from a business point of view. And I'm sure that some individuals would list their starting rating at 2800 just to get the initial bump. Trusting the honor system when no vetting of credentials is possible would be bogus and foolhardy.
Wow, a lot of people are missing a lot of points here.
Your opponent's average rating and your average score against them (ergo # of wins, draws, losses) is just a statistical nicety. People improve, often by a large amount, over time, so their earlier results aren't reflective on their current level of play. The fact someone scored 50% against 1800s 2 years ago is meaningless if they are now scoring 50% against 2100s - but the 50% against 1800s will still be inbuilt into their win/loss/draw vs average opponent rating score.
As for 1200 being an arbitrary starting number - yes it is. But this is where the Glicko system comes into its own... you have a very high RD, which means your rating varies much more wildly in your first few games. This allows you to move *quickly* towards your 'correct' rating, and as you play more games the rating changes you get for results decrease, to reflect the increased stability of your rating.
A new 1200 player might get (say) 300 points for beating a 1500 player, but that same 1500 player WILL NOT LOSE 300 POINTS. The 1500 player will lose whatever he would normally lose to a 1200 player (40 points say). You might think this would create discrepancies in the average rating, but remember that if that same new 1200 player LOST to a 900 player, he would lose 300 points while the 900 player would gain 40 points. So it all nets up to about the same.
The rating system is definitely important for playing matches of about your level. For people near the middle of the range it doesn't matter so much, but if you are rated highly (2000+) you do not want to be constantly playing players who are much weaker than you. This is not some form of arrogance - simply a player wants a hard-fought, even battle against someone reasonably near his strength. Without ratings, a 2000+ rated player would have to play hundreds of 1200 players and beat them all very easily, and this would be no fun for either player.
One more point about playing people rated much lower than you to artificially raise your rating. This is a complete fallacy. You get better rating from playing stronger players than you. Yes, if you're 1600 it should normally be easy to beat a 1200 player, but the fact of the matter is that you have to beat the 1200 player 15 times for every loss. The risk/reward for playing players much lower than you is NOT beneficial to your rating. At the same time, it doesn't make you 'unrealistically' or 'artificially' strong if you get to 1500 by beating many 1200 players. If you manage to beat them so easily, clearly it indicates that you are so much better than them that you almost never lose.
It is a well known fact that in real-world FIDE ratings, 2700+ ratings are somewhat inflated by the fact that they only play amongst themselves and very very rarely against players less than 2650. You will find that where 2700+ players mix with under-2600 players in tournaments, the higher rated players' ratings often suffer, because it is actually very hard to achieve the expected high score against people considerably lower than you.