Born in Lock Haven, Pennsylvania, Benfer was the son of a prominent Evangelical minister. Benfer became a five-sport star athlete at William Penn High School. He became the first York County basketball player to score 1,000 points in basketball. His 1,101 points scored for William Penn High School, including 531 points as a junior, was the school's career scoring record for nearly 70 years, and he also set the school's single-game scoring record with 50 points against Steelton on January 6, 1911. Benfer was also a star for William Penn's football team for three years and played goalkeeper on the school's first soccer team in 1910.
After graduating from York High School, Benfer enrolled at Albright College in Reading, Pennsylvania. At Albright, he played football, basketball and baseball. He played fullback for the football team and was selected as a first-team All-American fullback in 1914 by the Philadelphia Evening Bulletin. He was also named Albright College's "Athlete of the Century" in 1956.
Benfer later worked as a teacher, coach, and administrator for 50 years. He also played baseball for St. Louis Cardinals' farm teams for two summers. He was the basketball and baseball coach at Bucknell University from 1918 to 1919. He then returned to Albright College where he served as the athletic director and taught Latin and history until 1925. From 1925 to 1965, he worked at Muhlenberg College as a teacher of religion and a coach of football, basketball and baseball. He was also Muhlenberg's director of admissions from 1935 to 1963 and the director of men's dormitories until his poor health forced him to retire in August 1965.
He was also known for his work on behalf of American Legion baseball. He served as chairman of the Pennsylvania American Legion state championship tournament.
Benfer died at his home in Allentown, Pennsylvania in January 1966 at age 73. He was survived by his wife, the former Mabel Hoffman, and a son, Robert H. Benfer.
As a tribute to Benfer, Albright College awards the Haps Benfer Trophy to an outstanding student athlete each year, and Muhlenberg dedicated Benfer Hall, a men's dormitory, in the fall of 1965. In 1963, he was also inducted into the Pennsylvania Sports Hall of Fame in Hershey, Pennsylvania.