Castle is a gem of a series: the tone is fun without being slapstick, the plots are serious without being boring, and the characters are wonderfully written and played. On the outside, it's yet another Cop + Random Expert show: Detective Kate Beckett works murders in New York; Richard Castle is a popular crime thriller writer with influential connections, who has just killed off his most famous character. A series of murders based on one of his books occurs, and Beckett goes to him for help. They don't get along - she's sharp and no-nonsense, he's laid back and imaginative - but they solve the case. Castle then decides to write a new series, using Beckett as inspiration, and gets himself permanently assigned to follow her around, much to her disgust.
The Castle/Beckett relationship is the heart of the show - they bicker, they argue, and yet they find they need each other. There's the inevitable romantic tension, but the show cleverly never lets it go too far. The murders they solve are as interesting as anything in other cop shows, and can be quite dark at times, but the fun is in how Beckett's police work runs up against Castle's annoyingly good intuition. The balance of the humour and the murder is extremely tricky to pull off, and the show gets it right time after time.
The other characters in the show aren't neglected either. Ryan and Esposito are junior detectives on the team, and although often in the background are well rounded and get good dialogue. Castle lives with his teenage daughter Alexis, who is sensible, mature, and generally more grown up than Castle. He is also lumbered with his mother, Martha, a dramatic social butterfly who occasionally pauses to give Castle some pithy advice on life. The use of his family really helps ground Castle as a character, and emphasises that he's just a tourist to the grimy world of crime.
This first season is a short 10 episodes, so is really worth checking out. You'll get excellent actors, dialague, and plots for your trouble.