Y is an abstract strategy board game invented by Craige Schensted (now Ea Ea) and Charles Titus. It is a member of the connection game family inhabited by Hex, Havannah, TwixT, and others; it is also an early member in a long line of games that Ea Ea has developed, each game more complex but also more generalised.

Y is typically played on a triangular board with hexagonal spaces; the "official" Y board has three points with five-connectivity instead of six-connectivity, but it is just as playable on a regular triangle. Schensted and Titus' book Mudcrack Y & Poly-Y has a large number of boards for play of Y, all hand-drawn; most of them seem irregular but turn out to be topologically identical to a regular Y board.

Here is an image of the "official" board, sold by Kadon:



As in most games of this type, one player takes the part of Black and one takes the part of White; they place stones on the board one at a time, neither removing nor moving any previously-placed stones, and the pie rule can be used to mitigate any first-move advantage. A simple example board, 8 spaces to a side, with periods representing empty spaces:

         .
        . .
       . . .
      . . . .
     . . . . .
    . . . . . .
   . . . . . . .
  . . . . . . . .

The rules are as follows:

Players take turns placing one stone of their colour on the board. 
The first player to connect all three sides of the board wins; the corners count as belonging to both sides of the board to which they are adjacent. 
As in most connection games, the size of the board changes the nature of the game; small boards lend towards pure tactical play, whereas larger boards tend to make the game more strategic.

Schensted and Titus claim that Y is a superior game to Hex because Hex can be seen as a subset of Y; consider the following, with number signs representing Black stones and zeroes representing White stones:

        .
       . .
      . . .
     # # # #
    . . . . .
   0 . . . . .
  . 0 . . . . .
 . . 0 . . . . .
. . . 0 . . . . .

The portion of the board at the bottom-right can now be considered a 5x5 Hex board, and played identically. However, this sort of artificial construction on a Y board is extremely uncommon, and the games have different enough tactics (outside of constructed situations) to be considered separate, though related.

Mudcrack Y & Poly-Y also describes Poly-Y, the next game in the series of Y-related games; after that come Star and *Star.

The simple (regular) form of Y can be played by email, using Richard Rognlie's Play-By-eMail Server.

References
Browne, Cameron. Hex Strategy: Making the Right Connections. ISBN 1-56881-117-9 
"Game of Y." http://www.gamerz.net/~pbmserv 
Schensted, Craige and Titus, Charles. Mudcrack Y & Poly-Y.