I discovered the Jesse Stone movies around five years ago and just today started rewatching them. They are really, really good. Tom Selleck plays the brooding, man of few words police chief so well, and the background music really fits well with the overall melancholy, almost sad, theme of the movies. You defintely don't want to watch these to be uplifted.
Also the dogs in them are amazing. I think I posted about them here when I first discovered the movies. Between the acting ability of the dogs and the way they cut to them in the different scenes, they are just fantastic additions to the overall mood of the movies.
Anyway, highly recommended movie watching - just really well done for TV movies. Also, if you watch them, you don't want to watch in release date order. The second movie is really the first, so chronologically, you want to watch:
Jesse Stone: Night Passage (2006)
Jesse Stone: Stone Cold (2005)
Jesse Stone: Death in Paradise (2006)
Jesse Stone: Sea Change (2007)
Jesse Stone: Thin Ice (2009)
Jesse Stone: No Remorse (2010)
Jesse Stone: Innocents Lost (2011)
Jesse Stone: Benefit of the Doubt (2012)
Jesse Stone: Lost in Paradise (2015)