Which football player has made the most appearances for a single club?

Ryan Giggs for a major European top flight club.

As of 8th Aug 2012 he has made 909 competitive appearences for Manchester United, including 638 in the English league top flight.

Paulo Maldini has made 902 competitive appearances in a glittering career for AC Milan between 1985 and 2009 including 647 in Serie A in Italy.

For multiple clubs the record surely is held by Peter Shilton. He made 1237 appearences for 11 different clubs including 1005 league games in England. 849 of these appearences in top flight English League matches.