I think .. 32 games with Sporting Lisboa just ended today ( beaten by Porto eventually with a 89 min penalty ) on FM 10 .. cant remember from 01/02 till 09
FM08- 113 games with Celtic. (Unbeaten Streak ended in CL Final against Barcelona 2017/18)
FM08- 112 games with Newcastle (Unbeaten Streak ended in League Cup 3rd Round against Bury!) :-S
FM10- 32 games with Everton (Unbeaten Streak never ended, Save Game corrupted! Gutted! 2009/10)
if my memory serves me correctly my friend went about 250 with napoli in fm08 it was ridiculous, he had a wonder team though and i think the streak didnt start untill 3 or 4 seasons in but it was massive