On Natsume's Book of Friends
Extracted from Aroduc's 2011 Summer Anime preview:
A series that seems to inspire one of two things in people, an intense love [...], or the compelling urge to take a nap.
However fond I am of Natsume Yuujinchou, I have to more or less agree with Aroduc here. NY is pretty much a bunch of heartwarming slice of life stories that just happens to be about the supernatural (or mostly about the supernatural). Given my usual tastes, I have no idea why I like it so much, and I certainly can't recommend it except very selectively; it would bore or annoy a great many people.
(But if quiet, heartwarming stories about the supernatural sound like your kind of thing, you really owe it to yourself to check it out. Consider this a strong plug. You could probably start anywhere without losing much, but starting at the beginning of the first series isn't going to hurt.)
The military in Infinite Stratos
If IS' military use is prohibited, what is that destroyer doing in the academy's harbor?
If I take IS's background seriously I have to conclude that the whole 'IS military use is prohibited' thing is propaganda, and not very convincing propaganda at that. IS are armed, IS pilots are taught weapons and combat operation, competitions between IS pilots are combat duels instead of any number of other plausible tests of IS pilot skill, IS piloting seems heavily militarized, and so on. I can't think of a single non-combat use of IS we see in the entire series.
If I try hard, I can make the background covered on the Wikipedia page (see also) make some sort of sense. Clearly 'IS will never be used in combat' is a highly unstable balance of power that no one expects to actually last once things get serious, so everyone is frantically trying to get powerful ISs and stockpiling trained pilots (and keeping a careful eye on each other).
(When I was watching the series, I just assumed that there was some secret menace lurking in the background that some of the adults knew about and that all of the IS pilots were being prepared to fight, perhaps alien invaders or something. The IS anime ended right about where I'd expect the big reveal about this to happen in a longer series and I have no idea what happens in the light novels.)
PS: I try not to think too hard about the background in Infinite Stratos. The claimed lack of military use is just one of the issues that are probably best not examined too closely.