The Mentalist (2008-2015): drama about a fake psychic working with the police
I concur. That's a good one. I wasn't thinking of series that have already ended. Note that The Mentalist
has an overarching storyline that proceeds from the first episode to the last episode, so watch 'em in order. Definitely start with the very first episode.
Another one that has ended but was really good is Person of Interest
. It also has a cool sci-fi artificial intelligence twist to it in the later seasons. It also has an overarching storyline, so it is best watched in order.
and Without a Trace
from the '00s were good too. If you have a Roku, they are both available for free (with advertisements) on the Roku Channel. They may well be available free-with-adds elsewhere too.
There was a good series called Moonlight
about a reasonably-human-friendly vampire private detective. It only lasted a single season. I believe it is available for free (with advertisements) on one of the CW Network apps on the Roku. If you don't have a Roku, this CW Network app might be available on other devices.
was broadcast this century. So was In Plain Sight
. And Saving Grace
. And also The Closer
and its spin-off Major Crimes
. And Rizzoli & Isles
. All of them are good.