There's an important distinction that needs to be made here. Woodrow Wilson's will did not say that she could never marry. Rather, it says:

[Estate is left to his wife], and with the direction that my daughter Margaret shall receive out of the income of my estate, so long as she remains unmarried, the sum of twenty-five hundred dollars annually....^1

In other words, she continues to receive the money until or unless she marries. This is an important distinction, because a total restriction on marriage has always been void in the United States (at least on paper, although this gets more complicated as discussed below).

In England (from where the United States got most of its legal system initially), ecclesiastical courts were the ones who handled the personal property elements of wills. This would continue in England until 1857, when civil courts were established and given jurisdiction for this (among other things). Meanwhile, will transfers involving real property (i.e. land) were handled by common-law courts. The ecclesiastical courts did not allow restrictions on marriage, something they had in turn inherited from Roman civil law. They generally considered any restraint on marriage to be malum prohibitum, and would throw out the restriction (but leave the bequest itself untouched). On the other hand, common-law courts allowed "reasonable" restraints on marriage; but even then they were constructed strictly, meaning as narrowly as possible.

The distinction ended up being about whether it was a total restraint on marriage, or something more limited. The former was void, even among the common-law courts. On the other hand, a restriction on e.g. a timeframe, or prohibiting the devisee (the person who inherits) from marrying one specific person, were okay.

In the United States, the common-law version is what came across, so "reasonable" restrictions were okay. On the one hand, you had the now-cliche support for marriage. As one court wrote in 1857:

The family is the ultimate foundation upon which the soundness of the structure of the State depends.^2

But even then, as of the time that Wilson died in 1924, the conflicting precedent meant that it was often a matter of language. As one commentator wrote in 1939,

A testator using the phraseology of a limitation could obtain the practical effect of a restraint on marriage. The distinction between a provision granting a devisee an estate "until she marry", and a provision that the estate is granted "on condition she remain unmarried" is shadowy.^3

Moreover, such a provision "was constructed as showing an intention to provide for [an unmarried woman] while she was unmarried and not as a condition in restraint of marriage."^4 This presumption went back at least as far as the mid-19th century, as the cases cited in support were handed down then. I was also able to find a case from the District of Columbia Court of Appeals on this topic. It was decided in 1987, but at issue was a trust formed in 1938, which included the following provision:

No share of the income or division of the corpus of the estate hereby created shall be made to any beneficiary hereunder if, at the time such payment or distribution shall, by the terms hereof, be due, such beneficiary shall have married or be married to any person not of the Jewish faith or religion.^5

The appeal is on some subsequent issues, but the district (lower) court had upheld this as a "valid, partial restraint on marriage," and no one disputed that on appeal. I mention D.C. because that's where Woodrow Wilson was living when he died.

As I said, I'm not aware of any formal survey of how often this happens, but it was something courts and legal scholars have dealt with extensively over a couple of hundred years (the journal articles I cite below include numerous case citations), which indicates that it's an ongoing practice.

Citations

^1 Herbert Collins and David Weber, The Wills of the U.S. Presidents (1976), p. 176. Note that while this is the cite that Wikipedia uses, I pulled the full text from The Internet Archive (where it may be borrowed for free).

^2 People v. Olmstead, 27 Barb. 9, 33 (N. Y. 1857).

^3 Rose M. Trapani, Conditions in Restraint of Marriage, St. John's Law Review vol. 14, issue 1, pp. 94-95 (7-8 of the PDF) (1939).

^4 Id. at 94 (p. 7 of the PDF).

^5 Himmelfarb v. Horwitz, 536 A. 2d 86 (D.C. Ct. App. 1987). See also Gordon v. Gordon, 124 N.E. 2d 228, 230 (Mass. 1955) (upholding a provision that revoked a gift for someone who should "marry a person not born in the Hebrew faith"); Shapira v. Union Nat'l Bank, 315 U.S. 2d 825, 826 (Ohio Ct. Com. Pl. 1974) (upholding a condition that the gift is only given if the beneficiary married "a Jewish girl whose both parents were Jewish" within 7 years of the testator's death).

General Sources

Rose M. Trapani, Conditions in Restraint of Marriage, St. John's Law Review vol. 14, issue 1 (1939).

Ruth Sarah Lee, Over My Dead Body: A New Approach to Testamentary Restraints on Marriage, Marquette Elder's Advisor, vol. 14, issue 1 (2012).