This series really is fantastic its challenging, thought provoking, dark, funny and inventive throughout. The show never gets stale or predictable which is quite stunning when it starts of as a seemingly low key series involving the investigation into a violent street punk attacking random members of public with a baseball bat.
The other reviewer was spot-on regarding the quality of the writing and of the animation. The late, great Satoshi Kon could have conceivably made this as a live action series though I think Kon's use of the animated medium adds a lot to the story and atmosphere that live action cannot match, especially in regard to the many grotesque and creepy characters you meet throughout the series.
If your new to anime or feel it may be throw-away or low brow then this series is highly recommended. Paranoia Agent really is high quality stuff, I would say it stands up very well to some of the great live action TV shows like The Soprano's, The Wire and the like. basically if you like intelligent 'HBO quality' TV shows then please give this series a try and I'm sure you'll be impressed.
Note - I generally prefer to watch the subtitled versions of non english language movies and TV shows so I don't know how well its been dubbed into english - sorry