The Melancholy of Haruhi Suzumiya is a mish-mash of many genres. It includes paranormal elements, comedy, a touch of ecchi, and some slice of life. The different elements of the series blend well, resulting in a fun, if slightly unusual anime.
I tend to think of story in terms of overarching plot and certain key elements (climax, themes/motifs, pacing). Melancholy does not do so well in this regard, and it isn't intended to. The first six episodes (if you are watching in chronological order) have, by far, the most continuity. I found the pacing, order of events, and climax to all be satisfying in that part of the series. The remainder of the show, however, is more random. It displays the everyday life of Haruhi and her friends, without an overarching plot. Not that it wasn't enjoyable, but it won't win any points for plot.
I enjoyed the animation of Melancholy, for the most part. Coloring is well done, as are character designs. Don't expect the visual elements to blow you away, because they won't. They are just what I'd expect of anime with this development budget. It's really a matter of your tastes.
Initially, I didn't like Melancholy's opening and ending songs. Over time, though, they grew on me. The background music is decent, accentuating the scenes as best it can. Some of the catchiest songs in the series are God Knows and Lost My Music, sung by Haruhi in episode 12.
The voice actors are all acceptable. I prefer the original, Japanese seiyuu to their English counterparts; that, however, is my opinion. You may think differently.
Melancholy has an interesting cast of characters: an esper, time-traveler, alien, high school girl-turned-god, and Kyon (the one with absolutely no powers).
There is some character development, primarily in the characters of Haruhi, Yuki Nagato, and Kyon. I didn't see too much change in Mikuru (the time-traveler) or Koizumi (esper), however.
The variety of personalities is nice, but I felt that some of the characters could be more dynamic. I would have liked to see some character development in the aforementioned Mikuru and Koizumi. In the case of the latter, a touch of back-bone or conviction would be nice.
The Melancholy of Haruhi Suzumiya is a fun anime to watch. I recommend it to those of you looking for slice-of-life, paranormal, and high school elements. In conclusion: