Tecmo Super Bowl -- the only reason I still own a Genesis.
Madden 2K and 2K2 -- Most realistic football game I've ever played.
NCAA 2002 -- Based on the Madden engine, but with college teams. I love it. I've forsaken Madden to play it. You've got 32 teams in the NFL, but 117 teams in NCAA 2002!
NFL Blitz (any year) -- The "Smash TV" of Football
I can't remember the name of the arcade game, but it was similar to NFL Blitz, but an old game (like late 80s), and if you hit someone hard enough, the guy would start screaming, "MY KNEE!" and lie on the ground writhing in pain. I liked that game too.
And another game I can't remember the name of...it was a futuristic football-type game. You played with robots, and you had to pass the ball within a few seconds of snapping it, or else it exploded, then you had to get it past a 1st down marker, or else it would explode. That was a fun game as well.
And I pumped many a quarter into the ol' 10 Yard Fight machine. I could never get past the Pro Level, though. I did find it as a ROM and played it on my PC recently using an arcade emulator program. Still fun.