Here's the main competition, and their potential weaknesses:
In the East, the Giants and Eagles will be the competition, and as Alexander mentioned, winning the East and securing home field is paramount:
Giants - their offensive line is being shaken up a bit (Beatty to LT, Diehl to LG, Seubert to the bench), but Kareem McKenzie is rapidly aging, and there's no replacement for him on the roster. On defense, they will be changing the coordinator (Perry Fewell), and playing more cover 2 schemes. They have gaping holes at two LB positions (MLB and SLB - Kiwanuka and Sintim are not good fits here because they don't play well in reverse - a key in the cover 2). Despite adding Antrel Rolle, their success in the secondary is hinging a lot on Kenny Phillips recovering from knee surgery, which has been slow to this point. Aaron Ross is made of glass, and the backups are not great.
Eagles - Despite the changes, they have some questions with Kevin Kolb and LeSean McCoy. Neither guy has much of a track record in the NFL (McCoy has a little bit), and they will be critical to the team's success. This is the lynch pin for them. If they can effectively replace McNabb and Westbrook, then they will contend. If they can't, they will be .500 or worse. The defense cannot carry them anymore.
Outside of the NFC East:
Green Bay - Possibly the favorite to win the NFC. They are young and relatively deep at most positions except one - cornerback. They have a lot of age, and one player coming off of knee surgery at age 35. If Al Harris isn't the Al Harris of old, then they will have problems. Their pass rush isn't varied enough to make up for poor coverage in the secondary.
Minnesota - Two issues here. If Favre doesn't return, they aren't in any conversation about contending. Second, depending on how the Star Caps case turns out, if the Vikings lose the Williams Wall for four games, their hopes at home field will go up in smoke, as will their chances to contend. Their cornerback situation is even worse than Green Bay's, with Cedric Griffin coming off of an ACL and Winfield breaking down.
New Orleans - Their defense is still weak, and with the Vicodin distraction, I see this as being a nightmare season for them.
Carolina - I see them surprising people quite a bit. Their style of play will keep them in a lot of games, and with Fox fighting for his job, I see them being a bit more inspired. If Matt Moore or Jimmy Clausen can protect the football, I can see them rebounding to win the NFC South.
San Francisco - Potentially the best of a bad lot out West. Their draft went a long way toward reshaping their offense, giving them an even greater ability to pound the ball on the ground. This will help Alex Smith out a lot. On defense, adding Navorro Bowman will give them two rangy active hitters at inside LB. Their safeties are not good, and they need more of a rush from Ahmad Brooks, Parys Haralson and Manny Lawson, but they have been building for this. In a lousy division, I see them winning it.
In short, the division for the Cowboys and Green Bay are the toughest competition. If the Cowboys offensive line stays healthy, this could be a fun year.