One thing I've noticed over time is that shows where the setting is just ordinary life generally don't grab me, regardless of their genre or premise. This isn't an absolute rule and there are some exceptions (Toradora is one recent example), but the exceptions generally have to be very good. Add something out of the ordinary to the setting and the show has a much higher chance of getting my interest. The usual spice that anime uses is some supernatural elements, but a lot of things will do; it just needs to be something out of ordinary in the setting, even if it doesn't have much an impact on the story itself.

Note that this has nothing to do with my view of the quality of the show or whether or not I like them. I don't dislike (or like) such shows, I generally just don't and can't get interested in them.

One useful example is Natsume's Book of Friends, which is basically slice of life with supernatural elements. Without the supernatural elements, with the stories recast with normal people (which I think would be possible), I probably wouldn't have given the show a second look; with them present, I really quite liked Natsume.

I know that other people differ in their tastes here; for example, I suspect that Author is probably diametrically opposite my tastes in this. Also, given how many shows use ordinary life as their setting, I sometimes sort of wish that I didn't feel this way.

(There is something to be said for using ordinary life as the base setting for your show, because it means that you can concentrate purely on your genre and premise without the distraction of an unusual setting. If you don't need flying cats in order to tell your story, why put them in? (On the other hand, sometimes they're essential.))