I am pretty surprised at some of the takes on Ogletree in this thread. He was quite good as a Ram, albeit he did have his drawbacks. Arm tackling, as has been noted, was likely his biggest weakness. It cost us vs. the Falcons in the playoffs and I think that is distorting some peoples' memories of his overall body of work.
To his credit, Ogletree was an athletic linebacker who always brought high intensity and a good work ethic to the field (too much intensity at times, as he took some bone-headed penalties). Importantly, he also had a knack for making splash plays and causing turnovers. He was also very good in coverage - which makes sense, as I believe he was a safety at one point in his career (or perhaps I am thinking of another ex-Ram?). Obviously, I have no idea, personally, how he was in the locker-room. But I have read that he is well-liked by teammates and a good leader. Teams can use vets like that.
Worryingly, New York fans seem to suggest that his coverage skills have really declined in the past year or so. He's also a number of years older since we last saw him in horns. So some of his biggest assets - speed, athleticism, splash plays, and turnovers - might well have taken a decline, only to degrade further in the coming years.
Overall, the Rams are really weak at LB if we lose Littleton, which seems like it might be likely. If we don't draft a LBer high, I'd lump Ogletree in with all of the other FA linebackers out there - consider him if the price is right, when weighed against what other players are out there (and at what salaries).
Ultimately, I suspect that Ogletree will cost more than he's worth, with his best days also being behind him. But I'm still surprised so many have dismissed him summarily. "Go get a thumper", they say. Get in line with almost every other NFL team. The Rams do not have much cap room. We might well have to settle for whatever "plus" players are available, regardless of their genre, and pluck the guys that we think or system can maximize.