I pretty much agree with what has been said as far as the bigger derby games, but I'm also thinking... Southend v. Colchester Norwich v. Ipswich Swansea v. Cardiff Bristol City v. Bristol Rovers or Cardiff Heart of Midlothian v. Hibernian Portsmouth v. Southampton West Brom v. Wolves Swindon v. Oxford Sheffield Wednesday v. Sheffield United ...but to name a few. I would say it really depends on a persons view of what "biggest" means. Is it in terms of crowd size, violence, location, history, etc.?
The Old Firm, maybe then Liverpool/United, then Arsenal/Tottenham, or Newcastle/Sunderland. I think though "biggest" is simply the ones between the biggest clubs, which thus has the greatest media exposure. Luton Town vs. Watford has as much hate/animosity as Arsenal vs. Tottenham, but the media don't give a crap for obvious reasons, as Luton and Watford are very small clubs.