In the late 1960's Fischer, realizing the growth of theoretical computer science, established the ACM Special Interest Committee on Automata Theory and Computability (SIGACT, now the Special Interest Group on Algorithms and Computation Theory) and served as its first chair. Fischer also served as conference chair for the first five Symposia on the Theory of Computing (STOC).
Fischer taught at Harvard, Cornell, Waterloo, Penn State and Vanderbilt. In 1982, he was a target of the Unabomber. Fischer was away at the time but his secretary was seriously injured.
Fischer leaves behind his wife, Charlotte Froese Fischer, and brother Michael Fischer, both famous computer scientists in their own right. He also leaves a daughter Carolyn. A full obituary can be found here.
Update 8/31: New York Times Obituary