I'll admit that I originally skipped out on this one after seeing some promotional images of the animation style. However, I eventually decided to give this series a shot and it turned out to be quite a pick. Usagi Drop is a slice of life, but not a slice of life about making fun of ordinary events, rather a slice of life about what it really means to have a family and truly be responsible for another being. That being said, this is probably the first series that I'm ever going to recommend for older audiences not for profanity, violence, or scientific complexity but because of the actual content matter. If you're not old enough (mentally) you're just not going to find this entertaining.
While many other series these days tends to try to hide the parental aspect, this series boldly places it as the main theme. Usagi Drop takes a six-year-old girl and places her under the arms of her thirty-year-old nephew (her father is the main lead's grandfather...). The series focuses on parental issues ranging from time management to dealing with a sick kid. Yes, this means there's no secret agents, instant girlfriends, or anything else of the sort; as others have mentioned, realism is what this show is aiming for and, in my opinion, it does a good job of conveying it without making the material overly dry or intangible.
If you need your action/harem/ecchi/romance or are otherwise unable to focus on something, this is not for you. If you like warm shows that simply exist to brighten ones day (you don't have to be a parent), then you might consider this one.
Animation:
The animation is definitely unique, it was an initial turnoff but became OK as I grew accustomed to it. Every episode starts with a fuzzy sequence that looks like it was drawn with watercolors (pre OP). The animation then changes to a more typical style for the remainder of the episode. Overall the series has a slightly dulled look, sometimes under saturated, but perhaps this is to go along with the realism aspect. Backgrounds are dutifully drawn with no noticeable shortcuts used.
My initial turnoff was with the character styling, in particular I thought the styling looked a bit too plain. However, I still grew to appreciate the style as the show went on. Rin's furrowed brow look is by far the most memorable in this series.
Sound:
Thought the OP isn't really my cup of tea, it fit quite well with the slightly upbeat tonality of the series. The ED probably is a pretty good match as well though it was just too slow, ending a fairly uneventful episode with a sleep-inducing ED is just asking for a skip. Just don't forget that there's segments after the ED in every episode (some fairly good tidbits here). The BGM is just right as well, utilizing a wide range of instruments just enough to support.
This is probably the oldest role I've ever seen Kana Ueda take, but in this series Rin's VA takes the cake. They actually got a pre-teen girl to do her voice (for added realism?) and she did a tremendous job.
Story:
This show is progressive episodic. Each episode has a different topic, be it how to sign up for kindergarten or the difficulties of married life but time does pass- marked by graduations, growth, and lost teeth. It is truly refreshing to be able to reminisce about one's own past events, and to think of all the silly pranks one's done - there's a boy that Rin always plays with so guys aren't alienated.
While each episode is by itself quite interesting, it's really the character interactions that define the series rather than an underlying story. Indeed this doesn't really grow to any particular climax, nor does it have a conclusion. At the end, there's a lot of potential as to where the series could go (I've been told by others to just be happy that it didn't follow the manga...).
This show does focus on realism but as others have pointed out it isn't truly real. I found it a bit odd how Daikichi never really faced monetary issues despite having to take on Rin as well as getting demoted. Perhaps that would have tipped the scale towards the negative and shifted the focus away from the relationships that are the real focus of the show.
Character:
There's quite a few characters introduced in this series, but it's a manageable size and most of them are utilized fairly well. The majority of the warmth in this series radiates from the interactions between Daikichi and Rin, as they grow to accept each other. Daikichi and Rin are both dynamic characters and can definitely be seen changing through the eleven episodes. I really enjoyed the line where Daikichi philosophically asked whether he was raising Rin, or whether she was raising him.
If there was one character-based issue, it would be that Rin still seemed too mature for her age. Other than meandering off once in a while, she is able to quickly grasp complicated situations and is in general remarkably well behaved; all while maintaining that innocent smile of hers. Not to be too negative, but I have doubts that most children are like that.
Value:
You aren't going to find many other shows like this. Its combination of cute innocence and warmth create a very pleasant experience that will likely keep you watching. This is definitely one of those series where you can easily lose track of time, and to do so without resorting to action, romance, or anything out of realistic slice-of-life is quite the accomplishment.