For many people, Union Square is the main social center of New York. You can find farmer's markets, street performers (dancers, musicians etc.), people selling works of art and much, much more. But for me, the main attraction can be found at the south west corner of the square - the chess players.
From a distance they can seem a little unfriendly, but I can assure you this is not the case. As you walk past someone will shout out: "Chess player!" Or, "Can I get a game of chess?!" In loud, booming voices. If you feel up to the challenge and go over and sit down on one of the milk crates provided, they will introduce themselves and ask for your name. They will then offer to play with or without the clock. You will quickly learn that these people are by no means weak players, and, unless you yourself are equally skilled, you will probably lose very quickly.
The most important thing to keep in mind when approaching these people is that they don't play for free and they most certainly don't take any bullshit. If you approach them trying to gamble or play for free they will most likely either ignore you or tell you to clear off. Usually it's 3-5 dollars for a game, depending on the person. Most of the chess players are out there to make their living; for most of them it's their one and only job and means of making money. Some of them do have other jobs and come to play in their times off from work - they will usually be the ones who charge a little less per game.
Now I see that the way I have described them makes it look as if they're purely hellbent on money. That is a very inaccurate description. More than anything else - more than the money - they all love the game of chess, and love the competitive atmosphere in the area. People from local chess schools occasionally come there to try their skills against the seasoned players of the park, as well as general passers by and tourists. However, the chess tables are not just for skilled players and people who already know how to play the game. The players also all give lessons to children and beginners (sometimes for a little bit more money, but not always). This creates a great atmosphere around the tables. On the one hand you get high speed chess games between strong players which can often attract large crowds of people, but you also get children coming up eager to play, making a great contrast between education and sport.
Over the last year I have come to befriend a number of the regulars at the chess tables. If you're polite and normal around them and not pushy or nosy they will completely open up and will quickly become your friend. After being around them for quite some time it has become clear that they all specialize in different aspects of the game. Here are a few examples:
Sammy: Probably the strongest player at the square (possibly an ex GM... not sure) - Master speed chess player.
Omar: Extremely fast speed chess player.
TC: Fairly aggressive style of play, plays on a wooden board and has hundreds of possible game outcomes memorized in his head.
Rock: Teaches chess to anyone all over NY. All-round player with a very good endgame.
Thomas: Fairly defensive player. Excellent at teaching openings and general tactics. Very friendly.
While these people are out there to make money, they are also smart, skilled and funny individuals who are great to spend a day with (unless its winter... then it's just too cold).
One last thing... Don't take photos of them without asking - they find it very intrusive and it's a sure way to quickly piss them off. Also don't talk to anyone around a table when a match is going on... It's just plain rude.