This series rates 10's all across the board for me. The events and humour are random, the characters are awesome and the story is fun.
I watched this series in chronological order, not airing order, and I'm not sure if or how that would change perspective, but it probably does. It's hard to talk about the story because of it's randomness. The actual story arc focuses around the first 6 (chronological, not aired) episodes. The rest of the series employs random humour and more character development, especially for Haruhi. It combines humour, supernatural happenings, emotions and story in a really wonderful way.
Character:
Perhaps the best quality of the show are the characters. Kyon, unlike many male characters in his position, is a really great character. He narrates the story when needed, and tries to be the voice of reason in the group, but is generally overruled by Haruhi and ignored by the others. He tries to be really serious, even when narrating, yet he still finds himself coming back to the SOS Brigade headquarters every day.
Haruhi herself is a bit of a mystery. She starts off quiet and ignores everyone, but when Kyon takes an interest in her, she starts to open up and show her crazy side. She's not afraid to go after what she wants, even when it involves using her friends (mostly Mikiru) as the means to an end. When she doesn't have her way, the world is generally at stake. Kyon is the only one she'll listen to.
Koizumi is also a great character. He tends to just smile and go along with whatever crazy plans Haruhi has. Nagato is very serious with little personality and no emotions. She never interferes with Haruhi or anyone unless she has to, because she's there to observe.
Mikiru is almost a parody of the usual cute, dumb big busted girl character. She is that character, but she's forced into the fanservice situations by Haruhi, who does it for her own gain. Mikiru is very quiet and shy, and gets embarrassed very easily. She's also naive and really skittish. She's probably my least favourite character, but still enjoyable.
It's hard to imagine anyone not enjoying this series, and is definitely worth the watch! It now ranks among my top anime series!