To add to OP's question, 17 seems to also be somewhat common for eligibility for military service.

Twenty-one has always been the age of majority in the common law tradition of England and the United States. The change to eighteen is a relatively late phenomenon, legally speaking. Here's an example where the idea is basically taken for granted:

"Appellees contend that the intent and meaning of the phrase "age of maturity" is synonymous with the age of discretion and capacity and ability to think and reason for one's self. The appellant contends that the phrase "age of maturity" in this last will and testament means when the infant becomes an adult, over the age of twenty-one years. There are no disputed facts.

Commercial Bank & Tr. Co. v. Noble, 112 So. 691, 691 (Miss. 1927).

Another good example is the Rule Against Perpetuities. This is a rule which was created as a matter of legal tradition, not by legislation, and it functions to limit the "dead hand" power of testators disposing of their property through a will. We want you to be able to plan your estate and give your gifts as you see fit, but we don't want you destroying the marketability and commodity-status of real property by exercising indefinite control from beyond the grave. So, you are allowed to attach conditions and restrictions to things which must occur (if they occur at all) within the lifetime of people alive when the testator wrote, or twenty-one years after you die so you can give your heirs a chance to become legal adults before you give them stuff.

Here's an example of that reasoning, and you can again see how twenty-one is taken for granted:

Subsequently the limits within which the contingency must occur were extended (1) to cover the time necessary for the birth of a posthumous child, where gestation actually occurs, as every life is to be considered as beginning at the time of conception, then (2) twenty-one years were added to provide for the minority of children in esse at the expiration of the life estate. Later the consideration of minority was lost sight of, and the period of twenty-one years was allowed in gross, without reference to an existing minority. The rule was developed entirely at common law. It was brought to America as part of the common law of England, and is imbedded in the common law of Pennsylvania.

Barton v. Thaw, 92 A. 312 (Pa. 1914)

The English case which established that rule was in 1664 (The Duke of Norfolk's Case), so the presumption must be at least that old. Given the conservative nature of English common law, it's probably substantially older than that.

Here's one more, where the age of capacity to enter into a binding contract is presumed to be 21:

her infancy renders the joint conveyance not void but voidable, and vests the title to the land in the grantee, subject to the female grantor's right of disaffirmance upon her arrival at the age of twenty-one years, and until divested by some act done by her to disaffirm the contract

Scranton v. Stewart, 52 Ind. 68 (1875)