According to Official Guinness Records,
The record for the largest collection of board games belongs to Jeff Bauspies (USA), with 1,531 different board games as of 19 August 2011, which he has been collecting since 2000.
Some of the more interesting titles are: Stick it to the IRS! Chicago's Great Blizzard and "Coup d'etat".
For a complete list of 2011 records, please visit 2011 Guinness Records in United States.