I've been teaching myself Japanese over the past six years or so, on and off, extremely sporadically; I've never taken a single class, and, until I discovered Jim Breen's online dictionary, my only tools were a simple dictionary, a basic grammar, and a fairly comprehensive kanji dictionary. Fortunately I'm good with languages, and I've had fairly good exposure, being a mild anime nerd. That isn't the point, though.
What all that amounts to is that I've never had a comprehensive explanation of all the different verb endings. The ones I do know I understand quite well, but some of the subtler ones escape me. A good example is 見られる. I have no idea what effect the -areru ending gives a verb, but it seems to be a subtle enough one that I've never been able to pick it up from context. Similarly, I'm not entirely sure what the function of してる is; it seems alternatively to fill similar roles as する and して, but other than that I can't pin down whatever kind of nuance it's supposed to introduce.
While I'm very comfortable with most of the endings, feel free to explain anything that's comparably rare, subtle, or complicated. I'm sure there are plenty of others who have at least one verb ending they're unsure about, after all.