Minami-Ke has a second season.
Kyou no Go no Ni is good. (A lot like Minami-Ke, but it's an OVA).
More on the slice of life/romance side, I'd suggest True Tears and H20 ~Footprints in the sand~ (Both have plots to them though)
Hm. More dramatic, but Clannad and Kanon are both very excellent. (Clannad tells a story. Kanon has a plot).
If you like those kinds of shows, I think you'd also like Bamboo Blade. It's very good. Action/comedy about Kendo. I highly recommend it.
A few others to look into:
I My Me ~Strawberry Eggs
Myself; Yourself
Canvas 2 (It's a second season, but I never watched the first lmao)
Onegai Twins
Da Capo - VERY highly recommended. One of my alltime favorites. Made me physically sick because it was pretty emotional though, if that makes sense.
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