The Bengals were one of the biggest surprises last season, especially their defense. Unfortunately, their defense was probably the most significant fantasy contributor from this team. The really don't score enough to make their kicker valuable, but there is a good chance that there will be a few solid fantasy contributors from this team.
In my mind, BenJarvus Green-Ellis is very similar to Cedric Benson. If he can get the same 270+ carries that Benson got last season, he should dish out 1,100 yards and 6-8 touchdowns. I really can't imagine this guy breaking out and having a huge season, but he is good enough to earn the starting job for the Bengals. There really isn't much to say about this guy. He should be a flex runner who will score you decent points most weeks, much like Benson did. He should stay healthy throughout the season and can catch the ball out of the backfield, but he will probably be a 2 down back. The Bengals did not throw to the running backs very often last season, but there is a possibility that could change this season. In all, I wouldn't put a whole lot into this guy because you probably aren't going to get a whole lot out of him. Just being honest.
The same is true of Andy Dalton. He had a very efficient season last year, but he didn't put up exception numbers. I'm not saying that he doesn't have the ability to score big fantasy points, but I think he will slowly creep up fantasy drafts boards as he matures. My guess for him would be 3,700 yards and 25 touchdowns, with those numbers increasing over the next 3 seasons. He is definitely a solid back-up QB, but he is better behind someone like Tom Brady or Aaron Rodgers, where you really don't expect him to compete for a starting job. If he does have a great year, you can always trade him or trade for him, but I can't imagine him having a spectacular campaign. Maybe he will prove me wrong, but I doubt it.
The most valuable portion of this offense will almost certainly be their pass catchers. A.J. Green had an amazing rookie season and owners will look for him to be a low end WR1 in most leagues. Green and Dalton will have a real offseason to work on their timing and trust, which should lead to a lot more contested throws in Green's direction. He is a big, physical receiver (much like Dez Bryant) who should be able to push around most of the corners in the NFL. His injury plagued season is a bit worrying, but the fact that he played through the injuries is a positive sign for his toughness and passion for the game. He is a strong candidate to score top-10 receiver points this season. The second most valuable receiver on this team is going to be TE Jermaine Gresham. Gresham never really impressed me last season, and he will almost certainly fall into the big cluster of TEs at 750 yards and 6 touchdowns. The difference is that Gresham is entering his third year and has great potential, if he wants to use it. This is the NFL season of potential, where every player has infinite upside. I really don't see Gresham in the top 10 tight ends this season, but he could sneak in. I'll have to see something from him in the preseason to draft him. Jordan Shipley will probably move into the WR2 role for the Bengals, but he isn't worth drafting. Brandon Tate is also an option, but the Bengals used him as a return man rather than a receiver last season, so he probably won't catch more than 20 balls this season.
This team really has the look of an 8-8 team, but they managed to squeak out a playoff berth last season, so anything is possible. Dalton and Green should have good seasons, but I really can't imagine the defense being as great as it was last season. They didn't generate enough turnovers last season, but they did have a nice draft class. We'll see how the new players gel with the players from last season.