It's the third in the revered Key/KyoAni trilogy of Air, Kanon and Clannad. "Sad girls in the snow" is the stereotype. They're emotion-heavy romances. This is actually Clannad Season 1, with Clannad Season 2 being the one that really gets the critical plaudits, but it's still pretty good.
Firstly, some background. Key (a label of Visual Art's) is a developer of video games and "visual novels", sometimes pornographic (but usually in a romantic way). Air and Kanon were originally adult games and only later got censored all-audiences releases, but Clannad was an all-ages title from the beginning. The idea behind these games is generally that you play a boy who gets to know a bunch of girls. These weirdos and broken birds generally need help. If you can find a way to help your chosen girl overcome their emotional problems and become a happier, less damaged person, then you might find romance.
Meanwhile Kyoto Animation (i.e. KyoAni) is the studio behind many, many highly regarded shows, such as The Melancholy of Haruhi Suzumiya and (a personal favourite) Love, Chuunibyo, & Other Delusions. And, of course, Air, Kanon and Clannad. Other studios have also adapted Key properties, mind you, with Toei having done the first Kanon TV show and the Air and Clannad movies. (The Kanon I've seen is Toei's, not KyoAni's.) There's also a Little Busters! anime, from J.C. Staff. However it's KyoAni that's famous for its Key collaborations.
That's a lot of build-up to a show that's best described as good. I quite liked it. Not brilliant, but entertaining and pleasant. They'll have to bust a few genre traditions to find a way to continue this story for a Season 2, though.
Anyway, what I was describing above was the game. The anime simplifies things. No one's interested in a harem solution, so there's only one romantic path even though our hero will be helping quite a few people. There's very little romance, actually. As the title was meant to suggest, it's a show about friends, family and relationships. (The scriptwriter thought "Clannad" was Irish for "family", but he'd been misled by the name of the Irish folk band of the same name.) This is supposedly high school, but everyone's so innocent (and, in some cases, feather-brained) that you'd probably guess they were only in junior high. Even after the finale's love confession, for instance, the main couple will be getting embarrassed about calling each other by their first names or holding hands.
Contributing to this is the huge-eyed art style. There are plenty of other anime like this and in fairness the boys are fairly normal, but the girls barely even look human. (If you see anyone cosplaying as Nagisa, for instance, her hair will look like an insect's antennae.)
I'd better run through the cast. They're the show's heart, after all.
Tomoya Okazaki is the protagonist. He's a delinquent with a dead mother and a deadbeat father. The latter clearly isn't as bad as Tomoya thinks, but that's no consolation since Tomoya's life is heading for the toilet. He cuts classes, he doesn't care about his future and he'd reject any girl who tried to get close to him. What's going to save him will be his attempts to save his friends. He doesn't care about himself, but if someone's in trouble then he's quite likely to try to do something about it and hence unwittingly start dragging himself back towards humanity. He hasn't anything better to do, after all.
He's a bastard, though. He loves playing practical jokes on the gullible, especially his goofball best friend, Youhei Sunohara. Some of Tomoya's stunts are flat-out evil (but funny). He also no interest in social niceties, e.g. tact.
Meanwhile the girls include Nagisa Furukawa, Kotomi Ichinose, Tomoyo Sakagami, Fuko Ibuki and the twins Kyou and Ryou Fujibayashi. (Don't confuse Tomoyo with Tomoya.) Of these, Nagisa is by nature a passive shrinking violet, Fuko appears to have a mental age of six and Kotomi might be autistic. (They're all probably more intelligent than Sunohara, though.)
Oh, and Tomoyo's an ex-delinquent and Kyou's pretty violent towards Sunohara. He's asking for it, though. Literally. Repeated beatings don't stop him, either.
But then we learn about their stories. I love Fuko's arc, although apparently there are people who find it overplayed and strange. Personally, though, I think it's an extraordinary story of a kind I've never seen before, finding surprising emotional power despite being based around this freakish comedy character. I love Fuko. She's such a space case, yet so earnest and positive. She could pop out of nowhere and make me laugh, pretty much no matter what had been happening.
Kotomi is nearly as bizarre. Nagisa is normal-ish, but her parents are insane (but lovely) and Tomoko thought that Nagisa's dad's actions in ep.22 would make any normal daughter too embarrassed ever to be able to go to school again.
The world of all this is darker than I'd expected, albeit more so in the early episodes. (There's harsh stuff later on too, but some of the edge is taken off by the presence of supernatural story elements.) Delinquent protagonists ignoring their own futures will do that, especially when we're told that their mostly unemployed fathers are mostly into gambling and alcohol. And then we have the alt-universe OVA episode, "Another World: Tomoyo Chapter", which is set in a game route that didn't fit into the anime's story, but was also too powerful not to want to see animated. I wouldn't argue with anyone who called it the strongest episode of the series.
Oh, and I really like the closing Dango Song. It's different.
Do I think the show feels special? To be honest, no. Not yet. It's enjoyable and a fairly safe recommendation if you don't mind watching blob-faced anime girls who often seem younger and/or less mentally developed than their ostensible age, but at this stage I wouldn't say the show's putting a huge distance between itself and similar anime. This first season I'd call a nice, heartwarming high school anime. I liked it. I like the cast. It's often funny, but it's not a comedy. It contains romance (including a funny but brief period of polite, good-natured romantic competition), but that's not the main focus either. It's about relationships: friends and family. The show's childlike quality makes that more powerful, I think.