In 1967 there was a war between (suprise, suprise) America and Vietnam, a.k.a the Vietnam War. And obviously during this war, many people, or should i say many men, were being drafted and forced to enlist in the Army.
Among those many men was Muhammad Ali, the boxer and Heavyweight champion.
The only difference between those that were being drafted and Muhammad Ali was that Ali refused to take any part in this war. His refusal reason: "War is against the teachings of the Holy Qur'an(the holy book of Islam). I'm not trying to dodge the draft. [And] I ain't got no quarrel with them Viet Cong" . And for this reason he was accused of draft evasion, he was confined , his boxing license was revoked, and he lost his title as world championship.
Ali fought the courts for four years and on June 28, 1971(exactly 37 years ago): The Supreme Court overturned the conviction of boxer Muhammad Ali for draft evasion, finding that his refusal to fight in Vietnam is based on the religious principles of Islam.(http://encarta.msn.com/encnet/features/onthisday.aspx)
On a side note: I wonder if this would still hold today--to avoid the draft in a war because of your religious beliefs.