Well the Madden series i think are personally the best. That was my sole reason for getting a Megadrive and i used to buy those games year in year out.
I actually prefer the Madden 93 (Or Madden 93 Championship edition) which had much smaller graphics. Some of the later games werent too bad but i was never keen on the new graphic style.
An amusing game is 'American Football' on the Sinclair Spectrum. This was a strategy game against the friend or computer. It asked you for plays, eg SH shotgun and then the stick graphics would act out the play and it would keep stats. Back then (1984) it was excellent and despite poor graphics the gameplay is very good.
Also 'Headcoach' which is another Spectrum game (All available from www.worldofspectrum.org) is a very good strategy game. Strangely you only have 2 downs and you cant punt but despite very crude graphics (Was written in Basic) the strategy is very good.
You can trade players, cut players, draft players and act out regular seasons up to 100 years. Yet again back then it was very addictive and at times i still give this game a go.
However for me like i say the early Madden games on the Megadrive were the best