First of all, the term 'slice of life' is incredibly vague in my opinion. If you want to check out what wiki has to say about it, be my guest.
My interpretation is somewhere between the never ending elevator scenes in 'Neon Genesis Evangelion', and possibly something like 'Ghost Hunt', since it's timeline is determined by each new case (that has more to do with the 'slice' part of the term), or maybe the series 'NANA' which follows the life of two girls with the same name.
...It's seriously hard to pick a favourite when I'm not exactly sure what I've watched that classifies, but I think I'll go with 'The Melancholy of Haruhi Suzumiya'.
I know that in most ways, it's as far from 'normal' as it gets, but it would look normal, if you didn't know it wasn't....If you know what I mean.
Maybe 'Skip Beat!' is a better choice, but I'm very disappointed with where they chose to end the series, so no matter how much I love the story, that will always be a turn off.
