This list of detectives could be argued with. In fact, I encourage it because I’d like to be introduced to more like these fine sleuths.
Movies–

Clarice Starling from Silence of the Lambs. Smart, tough, and determined to find out the truth even if she attracts the attention of the psychotic Hannibal Lector.

Marge Gunderson from Fargo. You can’t much more girl power than the notably pregnant and clear-minded Marge.

Nora Charles of the Thin Man series. I adore Myrna Loy to pieces. As Mrs. Charles, she’s half of the best eccentric and happily married detective couple ever.
Books–

Nancy Drew – she of the titian hair in the endlessly and rightly revised book series. I remember loving the illustrations on the covers of Mystery of the Lilac Inn and Ringmaster’s Secret especially. I think she’s actually at her best in the computer game series made by Her Interactive. Cheerful, fearless, and relentless, Nancy is a force to be reckoned with.

Jane Marple of the quintessential cozy mysteries by Agatha Christie. Miss Marple is a magical crone who unerringly knows who is guilty and how to prevent more harm being done. My favorite Marple actress was Joan Hickerson.

Precious Ramotswe of the Ladies’ Detective Agency. Love the books by Alexander McCall Smith and loved the TV version with Jill Scott as the lead and the delightful supporting performance by Anika Noni Rose (also in Princess and the Frog and Dreamgirls).

Mrs. Emily Pollyfax is about the senior spy written by Dorothy Gilman. The author became cynical as the series went along but the early books are charming. (thanks Rose Kat for the correction)

Neil Hamel of New Mexico by Judith Van Gieso. A hard boiled detective wandering the mean streets of New Mexico. I lived near Albuquerque when I discovered this series and liked Neil and her much younger boyfriend quite a bit.
Honorable Mentions –

Thursday Next of the Eyre Affair. I liked Jasper Fforde’s literary-centric world but it was too rarefied for me. I am open to another attempt if anyone would make a case for it.

Stephanie Plum of the numbered mysteries (One for the Money, etc) written by Janet Evanovich. Irreverent bounty hunter solves mysteries.

Kinsey Millhone of the Alphabetic Murders by Sue Grafton. I never read past the first book of her lengthy series. However, I know people who love it.

Elizabeth McPherson. I love Sharyn McCrumb a lot but I think I prefer her non genre books better.