Brocksmith was born in Quincy, Illinois, the son of Vera Marguerite (née Hartwig) and Otis E. Brocksmith, who was a mechanic. He graduated from Quincy University in 1970. He then moved to New York City where he began a career on Broadway. His roles included Louis XIII in The Three Musketeers and the balladeer in a revival of Threepenny Opera with Raul Julia.

Brocksmith's nerdy, pudgy appearance made him perfect for comic roles, particularly in the late '80s and 1990s. Among his more prominent roles are the duplicitous Dr. Edgemar in Total Recall, a police sergeant possessed by Bill in Bill and Ted's Bogus Journey, principal Michael Oslo in Picket Fences and jovial mortician Irv Kendall in Arachnophobia.

He died in 2001, aged 56, from complications of diabetes.