Currently, my favorite anime is Sketchbook ~full color'S~. I got into it back when I was in a "slice-of-life" phase (specifically, three years ago), so it's reeeeeeeeeally peaceful and has very, very little action, if at all. As is to be expected of an anime whose main character is a shy girl that likes to draw and loves cats. Seriously, listen to the opening:
It's technically tied in my favorite anime list with Persona 4 The Animation, which does have action. Both shows are shows I like a lot, but I'd recommend Persona 4 to other people simply because it seems like an anime more people would like. Persona 4 The Animation is also currently airing, so new episodes keep being released, which is nice. Gives me something to look forward to.