The Big O is a mech anime in film noir style, that ran on Adult Swim for quite a while. In fact, it didn't catch on in Japan, but it was so popular in America that Cartoon Network co-produced the second season themselves.
"The television series is designed as a tribute to Japanese and Western shows from the 1960s and 1970s. The series is done in the style of film noir and combines the feel of a detective show with the mecha genre of anime. The setpieces are reminiscent of Toho monster movies and the score is an eclectic mix of styles and musical homages.
The story takes place forty years after a mysterious occurrence causes the residents of Paradigm City to lose their memories. The series follows Roger Smith, Paradigm City's top Negotiator. He provides this much needed service with the help of an gynoid named R. Dorothy Wayneright and his butler Norman Burg. When the need arises, Roger calls upon Big O, a giant relic from the city's history that may hold the key to its future."
-Wiki
In other words, Roger Smith uses this giant robot to fight things. Other giant robots, monstrosities, etc. And his mech fighting style includes a lot of punching things. The robots all look awesome and there's lots of buildings getting toppled. Also, Dorothy talks a lot of smack. I just bought this series in full and it's excellent. If you love classics and giant robots and film noir detective investigation type stories, you may love this.