It's obvious that key injuries can critically affect NFL teams (see: the 2011 Indianapolis Colts, and by extension, the 2012 Indianapolis Colts).
Despite the example of the Colts, there's always a danger of overfitting injuries to team failure. Injuries to Brandon Weeden and Colt McCoy -- serious as they are -- didn't keep the Browns out of contention by themselves (there's a whole host of things keeping the Browns out of contention, and the three biggest are the Ravens, Bengals, and Steelers).
But right on the cusp of success you can see that a team's collective health can really make a difference. Let's look at an example from the AFC. We'll compare the Steelers (8-8, 7th place in the conference, did not make the playoffs) with the Bengals (10-6, 6th place, made the playoffs).
(Stats and numbers to follow. Fair warning.)
When the Steelers went on their season-ending 2-5 skid, starting with a loss to the Ravens in Week 11, they looked like the gonorrhea ward after a political convention. They never had fewer than 10 names on their injury report (except for week 17, when they won a meaningless game against the Browns with only ("only") 6 guys limping). The Steelers played just 2 games all year with a full roster. On average through the season, the Steelers injury report had 9.5 names on it every week. That's 18% of your guys out or playing hurt.
By contrast, look at the Bengals. They averaged 8.25 guys on the injury report every week, and during their season-ending 7-1 streak never had more than 10 names on the report (and 10 names only once, in week 10). Through the season the Bengals never had more than 2 guys out, and had 7 games with nobody out.
And let's not overlook the most critical position. The Steelers were without Ben Roethlisberger for 3 full games, while Andy Dalton played every game for the Bengals.
The Pittsburgh sports intelligentsia -- by which I mean the callers to all four of Pittsburgh's drive-time sports call-in shows -- are pretty convinced that Roethlisberger wasn't anywhere near 100% when he did get back in, and the team's 1-3 record after his return suggests that they may be on to something.
Were the injuries the only difference? Of course not. The Steelers won a game for which they had 12 guys out or hurt (against the Redskins in Week 8) while the Bengals lost a game in which they only had 5 names on the injury report (against the Broncos in Week 9). But they may have made the difference in the margins here.