This is interesting because things get extremely different on state and federal levels.
Under modern U.S. law, suicide is no longer a crime. Some states, however, classify attempted suicide as a criminal act, but prosecutions are rare, especially when the offender is terminally ill.
The "some states" part is much more important than was emphasized there, however.
A case that reached the Virginia Supreme Court, Wackwitz v. Roy (referred to in Wikipedia) pivoted about the legality of suicide. From the decision:
We are aware of only one legislative enactment that addresses suicide as a crime. Code § 55-4 provides that "[n]o suicide ... shall work a corruption of blood or forfeiture of estate." Thus, although the General Assembly has rescinded the punishment for suicide, it has not decriminalized the act. Suicide, therefore, remains a common law crime in Virginia as it does in a number of other common-law states. See, e.g., Southern Life & Health Ins. Co. v. Wynn, 29 Ala.App. 207, 194 So. 421 (1940); Commonwealth v. Mink, 123 Mass. 422 (1877); State v. Willis, 255 N.C. 473, 121 S.E.2d 854 (1961); State v. Carney, 69 N.J.L. 478, 55 A. 44 (1903); State v. Levelle, 34 S.C. 120, 13 S.E. 319 (1891), overruled on other grounds by State v. Torrence, 406 S.E.2d 315 (S.C.1991).
To constitute suicide at common law, however, a person who takes his own life "must be of years of discretion, and in his *865 senses." 5 William Blackstone, Commentaries *189; accord Plunkett v. Supreme Conclave, 105 Va. 643, 646, 55 S.E. 9, 10 (1906) ("`To constitute suicide at common law the person must be of years of discretion and of sound mind.'"). This common law rule comports with a contemporary definition of suicide. Suicide is defined as "the deliberate and intentional destruction of his own life by a person of years of discretion and of sound mind." Webster's Third New International Dictionary 2286 (1981).
I believe that the "only one legislative enactment" refers merely to Virginia state law, not nation-wide law.
Thus, in Virginia, and other states, suicide could be treated as a common-law crime. However, in United States v. Hudson, it was ruled that such common-law convictions are not allowed at the federal level. I'm not always a fan of Google Answers, but the last one here provides a fairly well-documented section on common-law rulings about suicide. Note that in many states, this is not enforced, as common-law rulings are increasingly rare.