Which team has played the most games in a season since the English Premier League started?

These two teams:

63 by Manchester United in 1998-99

38 League
6 FA Cup
13 UEFA CL
6 League Cup
1 Charity Shield

63 by Liverpool in 2000-01

38 League
13 UEFA Cup
6 FA Cup
6 League Cup

If you exclude the annual Charity Shield match, it's Liverpool solo. Before the Premiership started in 1992 it's Arsenal in 1979-80 with 70 games:

42 League
11 FA Cup
9 Cup-Winner Cup
7 League Cup
1 Charity Shield

and behind them is probably Leeds United with 64 games in 1972-73

42 League
8 FA Cup
9 Cup-Winners Cup
5 League Cup

Source: Rothmans Football Year Book (now SkySports FYB)

Behind the Arsenal team of 1979-80 - Bobby Robson's Ipswich Town side of 1980-81 played a total of 66 games. Defender Russell Osman played every game.

Source: WSC http://www.wsc.co.uk/the-archive/918-Playing-the-game/3715-permanent-fixtures

Looking back 20 years we find one of the most tragic cases of fixture overload. Bobby Robson's brilliant Ipswich Town played 66 games with a group of basically 13 players and almost won a Treble. The majority of these players also played in World Cup qualifiers and Home Internationals.

Ipswich lost just two of the first 32 league games but seven of their last ten, missing the title by only four points. They lost an FA Cup semi-final in extra time but had enough left to win the UEFA Cup after a campaign that took in Prague, Salonika and four other trips. Paul Mariner and Mick Mills were still playing for England in Budapest in June.