Will charging a smartphone while it is in a case lead to damage? Will it harm my Razr to charge it while in an Otterbox case? I heard that would cause excessive heat which would damage the battery or shorten lifespan. True?
Heat and lithium ion batteries aren't the best of friends, so anything you can do to maintain a lower battery temperature will prolong your battery's life. While charging or under heavy load, you typically generate more heat than while resting, so in either of those cases, if your phone feels physically warm, it's probably a good idea to remove it from the case. However, if you're charging it somewhere that it's likely to be damaged by being knocked off a table, having something dropped on it, having a kid find and play with it, etc. then I'd be more inclined to keep a protective case on it. The life of your phone is much more important than the life of your battery, as a battery is much cheaper to replace (Note: I'm not familiar with how easy or difficult it is to replace the battery on a Razr, beyond knowing that it's not as simple as popping the back off and pulling the battery).

I'll add that while it's possible that a case (particularly the thicker ones like Otterbox produces) could lead to enough excessive heat that it damages the battery, I haven't heard of anything beyond a faulty battery actually damaging itself (think of the exploding battery stories). I would think that we'd hear a lot more about this if it were a significant issue.