Well this isn't part of a series but I found The Caine Mutiny by Herman Wouk a wonderful book. It takes place on a Navy warship during WW 2.

try "The Perfect Storm" . Even though it isn't fiction, it's still a great nautical read.

Voyage of the Narwhal by Andrea Barrett. I could hardly put it down.

Horatio Hornblower Series EM Forrester

"Moby-Dick," by Herman Melville (the author spent years at sea, and said his whaling ship was his Yale and Harvard.)
"Trustee from the Tool Room," by Nevil Shute (mild-mannered city man has sailing adventure in the South Pacific.)
"The Wreck of the Mary Deare," by Hammond Innes. A lost-at-sea mystery; the basis for a classic film.

Ahab's Wife by Naslund

Sailors worldwide revere The Riddle of the Sands, by Erskine Childers. And I think highly of Sam Llewellyn's nautical thrillers, though they're a bit bleak and black.