This is tough, since the NFC is much worse than the AFC. There could easily be three NFC teams with worse records than the worst AFC team.
NFC: I really want to say the Panthers, but everyone is calling that. The 49'ers are really going to suck, too. Both of those teams will be worse than the worst AFC team. I'll take a new one and say the worst NFC team this year is the Redskins.
AFC: The Bengals will be bad, what with their QB situation and not having a WR and getting rid of Dhani Jones (bad karma). With Chris Johnson back in the fold the Titans won't contend for worst barring a season-ending injury. Denver could really suck. I'm going to with the Dolphins are the worst AFC team this year. They don't have a good QB, they don't have good RBs, their only receiver is Brandon Marshall who is a headcase and pouts, their DEF is bad, they just got worse in every aspect of the game this offseason.
I will also predict that JAX will set the record for lowest attendance in the modern era over the course of a full season.