Aside from people who have already been mentioned, one from my school days, Sir Josiah Mason springs to mind. A real rags to riches story. Taught himself to read and write, and went on to become a captain of industry, as well as opening an orphanage in Erdington.
Also, although he had a tragically short life, it makes me burst with pride that Harry Moseley was a Brummie. A remarkable young man.