It depends which competitions/cups you count. The official record is 19, but I'm unclear what leagues/cups that included. So many leagues have changed over the years too which complicates things.
As far as I understand, if you count the 2 league cup-victories Sheffield Wednesday have in this 2012-2013 season (at the time of this post). Then Sheffield Wednesday are currently again 19 games unbeaten. So as far as I understand, if SWFC win/draw on Sep 1st 2012. That will be a new club record of 20 games unbeaten. If League Cup matches don't count, then obviously it will take 2 more matches to break the official league-title-games record. They beat Fulham, a premiership team that scored twice at Old Trafford a few days before for their 19th game unbeaten. Quite a scalp! They surely will continue their run.
6,000,000,000 games unbeaten
The whole season
The answer is Arsenal FC
Celtic.
Spain and Brazil had 35 games unbeaten each. As of 06.28.10, Netherlands has a 21 game unbeaten run
Chelsea
It is unknown which team has the longest unbeaten run in all competitions. Arsenal have the longest English league run with 49 games unbeaten, which included the entire 2003/04 Barclay's Premier League season unbeaten. Chelsea have the longest unbeaten home run in the league with 86 games. Liverpool have the longest unbeaten home run in all competitions with 85 games. The longest unbeaten League run in English Senior Football is held by AFC Wimbledon who went 78 games unbeaten from 22 Feb 2003 to 4 Dec 2004. This included a complete league season undefeated. Steaua Bucharest went 104 matches unbeaten between 1986 and 1989
i think it is Manchester uniteds 56 games unbeaten spanning 40 years
Longest unbeaten run (all): Celtic currently hold the UK record for an unbeaten run in professional football : 62 games (49 won, 13 drawn), from 13 Nov 1915 until 21 April 1917- a total of 17 months and four days in all (they lost at home to Kilmarnock on the last day of the season).Longest unbeaten run (home): Celtic also hold the SPL record for an unbeaten run of home matches (77), spanning from 2001 to 2004 (this run was ended by a 3-2 defeat to Aberdeen on 21 April 2004), and the record for the longest run of consecutive wins in a single season (25 matches).
Arsenal-14 in feb 2002 to august 2002.
The longest unbeaten run for Newcastle United Football Club is 11 games. This streak took place between August 15, 1992, and December 24, 1992.
Currently, 14.