Fulks was born in Birmingham, Kentucky, a small town in the state's far-western Purchase region that was inundated in the 1940s after the Tennessee Valley Authority dammed the Tennessee River to create Kentucky Lake. He played college ball at Murray State University for two years before leaving school to join the Marines.
Fulks joined the BAA's Philadelphia Warriors while in his 20s, and his team won the BAA title in 1947. During his career, he was considered the league's greatest offensive player. During his first three seasons, Fulks averaged 23.9 points per game at a time when, before the advent of the shot-clock, games rarely scored over 70 points. He won the league's first scoring title in 1946-47 with a 23.2 point per game average, and had a career best 26.0 per game average in the 1948-49 season.
The 6'5" (1.96 m) Fulks was known both for his athletic drives to the basket as well as his shooting. He was perhaps most remembered as one of the pioneers of the modern jump shot. On 1961 he was named NBA 25th Anniversary Team.
Upon his retirement he returned to Marshall County, Kentucky where he lived the remainder of his life. He was shot and killed during an argument with Gregg Bannister over a handgun on March 21, 1976.