I'll second the urging of Hammett and Macdonald. Hammett actually created the American hardboiled detective novel, along with such characters as Sam Spade, Nick and Nora Charles (
The Thin Man series) as well as creating the Continental Op. His style is somewhat more terse and a bit more dry (in the positive sense) at times than Chandler, but damned good, and gets better with repeated readings. Macdonald's first Lew Archer book is a tad uneven, but he hits his stride quickly, and even
Moving Target is well worth reading. It's a bit later in period, so it has a slightly different sensibility, but is every bit as meaty as the other two.
I'd also like to put in a word for another Macdonald... John D. MacDonald, with his Travis McGee novels. Not truly hardboiled in the same sense as the other three, but very closely related. Trav is someone who "finds" things that other people have lost... for a fee. He also has a bit of the "knight-in-shining-armor" to his personality, which he frequently curses himself for, as it gets him into some very nasty situations both physically and emotionally, as his cynicism about people wars with his innate idealism. The books are wonderful, even if occasionally a bit wonky in some passages; the flaws are minor blemishes, and if you like the sorts of things that come out of Marlowe's mouth, you'd almost certainly like McGee's take on things.
One thing all of these characers share in common is an innate decency and unspoken idealism about the human race that is constantly at war with what they do for a living, and the venality they see all around them... and frequently have to practice themselves. It allows them to be very keen observers of their society, and allows the books themselves to be wonderful stories and vehicles for examining the heartmeat of the human condition at the same time....
Here's the list of the McGee novels:
John D. MacDonald - Wikipedia, the free encyclopedia
As well as the Lew Archer stories (both novels and shorts):
Lew Archer - Wikipedia, the free encyclopedia
I'd suggest reading them in order, as this allows you to see the characters grow and change, as well as allowing you to see an arc of the writers' views of the world in which they live. And here's a helpful look at Hammett:
Dashiell Hammett