I've been lurking for a while and decided to sign up to respond to this topic, then I couldn't get my account to work for a while and the thread went silent since. My account is fixed now though (thanks Rui) so I can spend ages yammering on about my favourite type of anime (and maybe other people can get a word in).
I think Slice of Life is a pretty open category, most people include "Cute Girls Doing Cute Things" and it seems to be the most common (or commonly known) but I guess there are plenty of other things that count. I'm not sure what the restrictions are, some people say it should be set in the "real world" while some say that supernatural stuff is okay as long as it's mostly about the characters. I guess I lean towards a wide definition (which might be cheating), I usually prefer character driven/focussed shows so that's probably why Slice of Life tends to appeal to me.
One of my personal favourites is Aoihana/Sweet Blue Flowers. It's one of the few Yuri anime I've seen and I'm very interested in seeing more like it (which seems to be difficult, unfortunately). Maybe it's cheating to pick a Yuri show but one of the main reasons I liked it was because the characters and issues felt very real. From the way the OP described Glasslip I think there's a decent chance that they'd like this show too (and if so, it could open up a whole other genre at the same time).
Living For The Day After Tomorrow (I think the Japanese title is "Asatte No Houkou") is another one I'm quite fond of. It does have a supernatural element but I think it's quite a good look at the subject of "maturity" (or something along those lines) and I guess I just liked the characters.
I don't know if Shirobako counts as Slice of Life but I love the show anyway so I'm going to recommend it anywhere I can get away with it. It's the sort of show that can be something different to everyone, personally my favourite part was the characters and the "working life" elements but other people might like the look into how anime is made, the references to anime and those that work in it or maybe something else. The downside being that you might hate one element enough to let it spoil the show for you, which would be a shame. I think everyone should at least try Shirobako but it'd be best to go in without expectations because the elements that stand out for you might be different to what others experienced.
Probably moving closer to "Cute Girls Doing Cute Things" but another show I think is worth mentioning is Gingitsune. It's kind of a gentle daily life show but it does deal with some interesting topics along the way and it seems to often be missed (although Sentai released the Blu-ray recently, which is nice). Maybe it's often missed because it's tough to describe what makes it good, which often seems to be a problem with Slice of Life shows in general.
I guess Love Lab counts as "Cute Girls Doing Cute Things" but I think it's notable that it does have something of an ongoing story rather than the more episodic style that is common (though it has some of that too). I'm glad that more "Cute Girls Doing Cute Things" shows are getting sequels but it's a shame that Love Lab doesn't seem to be one of them.
I do like "Cute Girls Doing Cute Things" shows a lot so I'm glad that they seem to be getting more common. I suppose having more of them means it's more likely I'll find one I don't like but I've been pretty lucky so far. I'm really enjoying the second season of Kinmoza (Kiniro Mosaic) at the moment, I already liked the first season but I think the second might be even better (possibly because of the new characters and increased Yuri). Hidamari Sketch is one of my favourites, it and Azumanga Daioh got me addicted to this sort of thing. I do think Non Non Biyori is worth mentioning again too even if it has already been mentioned a few times, I'm really looking forward to the next season. I don't think anyone has mentioned A-Channel, it seems to be more divisive but I enjoyed it quite a lot (enough to buy the Blu-ray when I already had the DVD, although to be fair the Blu-ray was cheap anyway). I don't know if there could ever be enough of these shows for me.
Okay, I've gone on a fair bit. Last point for now, I'm not sure if the more philosophical shows like Mushi-shi and Kino's Journey count but I think I enjoy them for similar reasons at least. We get a slice of the main character's life and through their journeys we encounter slices of other people's lives too. I guess Natsume's Book of Friends/Natsume Yujin Cho is similar. It's a shame there aren't more shows in this style (although I guess they can be a hard sell).
