Brian Cashman has taken a lot of heat recently for having another roster of poor depth. But I have to disagree. The (probable) loss of A-Rod is more a fluke than anything else. You take the best player off any team and they all of a sudden look thin.
Outside of utility infielder, the bench is actually quite strong.
The two backup outfielders/pinch-runners/late-inning defensive replacements are one of Brett Gardner/Melky Cabrera and Nick Swisher/Xavier Nady. I'll go with Melky and Nady for now. Those guys could start on a lot of ML teams.
Nady has a career 108 OPS+, so he's a good hitter and about an average outfielder. Melky's not as good with the bat (84 OPS+), but makes up for some it on defense (with a plus-plus arm) and on the bases.
Jose Molina is the backup catcher. He won't hit much (still better than Wil Nieves and Sal Fasano), but he's one of the best defensive catchers in all of baseball, throwing out 43% of potential base-stealers. That is an absolute asset.
The pitching depth is superb. Phil Hughes is the sixth starter and is having a better spring than Joba Chamberlain. Two other potentially solid big league starters sit at seven and eight on the depth chart: Al Aceves and Ian Kennedy.
The bullpen will have several of the following high-ceiling players 'refining' their game in the minors: Dave Robertson, Phil Coke, Humberto Sanchez, Jon Albaladejo, Edwar Ramirez, and last but not least, Mark Melancon.
Admittedly, the utility infielder spot is a weakness. Cody Ransom/Angel Berroa are it (for the time being), neither of whom have either high-ceilings or good gloves.
Outside of that though, the depth is actually very strong.