K-ON! is an incredibly endearing anime, while it isn't particularly earth shattering, it is probably one of the best of its genre.
Story: The story isn't an amazing display of intricate story telling, but the anime is well paced, each episode has something going on and there aren't really any episodes where you feel like it was a waste of 24 minutes, nor does it become difficult to follow because of too much going on.
Animation: Kyoto Animation did a great job animating the series. The style is cute and captures the feeling of the series. And all the details, from the instruments to the backgrounds are captured well.
Sound: K-ON! was very well cast, the seiyuus do a great job capturing the characters. Even the supporting cast is terrific and The music cute and catchy, which fits the series wonderfully.
Characters: The characters are very endearing and memorable, and you will grow to love them throughout the series.
Overall: K-ON! is funny, cute, and endearing, it does a great job capturing the 4-koma it's based on, and probably exceeds it to some degree. It's not for everyone, but for those of us who love a good slice of life anime, it's certainly well worth watching.