I might be a bit careless in relation to spoilers.
Before reading novel series I had watched anime, two times. Basically, first volumes brought me almost nothing new. By the way, if somehow you haven't yet watched anime, I'd recommend you to start off with it first. Kyoani made an excellent job on it.

The story opens with a main character's monologue. Thoughts of Kyon which will guide you through all the chaotic mess awaiting you. So, one perfect day Kyon happened to think about talking to a certain girl... From this and now on, his life would never be the same. All the supernatural stuff he'd long time ago gave up on appear to be real.
It is done in such an engaging way. Supernatural stuff with a slice of life flavor. Or vice versa. What I really find great, it has a touch of sci-fi in it. Almost everything bizarre that happens doesn't remain unexplained. What's even more cool, there are several theories upon what is happening and it's up to reader to choose what to believe. The author is very good at leaving here and there tiny hints, which may provoke in you a huge line of thought or may not. Honestly, you may just leave it be and regard the whole series as a comedy.

You may refer to Kyon as being a link between SOS Brigade and readers. Story is told from his perspective. Basically, he's a narrator. I like this part. Slowly, you grow to understand and even befriend him. I mean, how couldn't you, if you're always inside his head. Sometimes even thinking about what he's thinking. If I were to describe him, first thing popping up in mind - nice guy, considerably smart. Still, it's a poor description, because there's something more to him. Or I just imagine things. Generally, I'm okay with the way Kyon is. I believe there's only one cliche problem with him. He doesn't get girls' hints. Well, otherwise there wouldn't be such an intrigue the whole series.

The series is built upon various interactions between characters. Every character is cool in his/her own way. Even though there're some cliche characters... they are cliche only on the first glance. Or not. Or cliche partially. However, I adore all of them. I won't be pretty much wrong calling Haruhi almost literally the Sun. Well, everything reloves around her in the series. And Haruhi is the type of character which will force you to like her or hate her. You can't possibly remain indifferent. As for me, I loved her. She's so damn simple and in the same way hard to follow. She always has some reasons for her actions. She's a weirdo but a smart one.
I think it'd be possible to create a separate story with every character of SOS Brigade on their own. Haruhi series went further than that, deciding to create a spicy mix. Mikuru, Yuki, Koizumi - all of them offer various perspective and feel to the story. New characters pop up rarely in the story. I grew so attached to SOS Brigade, that I even felt sceptic upon their appearance. Magically, they were another bunch of non-less cool characters. So, the chance of getting annoyed or bored with characters is low. Don't forget to check out 'Rainy Day' once you've finished series.

The setting is done in such a way that almost anything could happen. I can't help myself to praise time-traveling aspect of the story. It is not present in the story just for for sake of being present. It is a thick and good elaborated part. It simply beats roughly half of all time-traveling stories. Or even more. I can't say that for sure, it's just the feeling I got.

Can't say much about art, I mean illustrations. They are few. With every volume the quality of illustrations was better.

I really miss the series. Afterword of the last volume doesn't bring lots of hope. I just really hope Nagaru Tanigawa will get a grip of himself and will eventually resume writing. There's a lot more to tell.
Melancholy of Haruhi Suzumiya brought me a lot thoughts, sincere joy and many other emotions. It is extremely unboring and enjoyful. I could talk and talk more about it, but what's the point? Go just read it.

Please, Nagaru Tanigawa make a comeback. We are waiting.