The most common situation where this comes up is the right to a jury trial. In almost every U.S. jurisdiction, civil cases that would have been tried in a court of law in England in the late 18th century carry with them a right to a trial by jury, while civil cases that would have been tried in an equity court in England in the late 18th century are tried before judges without juries. (Despite the fact that modern English law restricts juries to only a handful of obscure types a civil cases today.)
Another situation where this comes up is the question of remedies. U.S. federal district courts, like most general jurisdiction courts in the United States, have the power to impose any remedy that equity courts in the 18th century could have imposed. One of those remedies is disgorgement, i.e. the power to make defendants pay an amount equal not to the amount by which the plaintiffs have been harmed, but instead to the amount by which the defendants have profited from their illegal activities. Today, the 2nd Circuit Court of Appeals finds (starting at page 16) in the case of SEC v. Cavanagh that the English equity courts had this power, and that as a result, Securities and Exchange Commission enforcement suits, which sound in equity because corporate disputes were governed by equity courts in the 18th century, is entitled to this remedy in suits involved securities frauds today. As a result, the Defendants must pay not only a $1,000,000 fine, but an additional $15 million+ of disgorgement of their profits from the frauduluent pump and dump deal they conducted.
Incidentally, history and law, always close cousins, have other points of intersection. For example, the U.S. Supreme Court in the early American Republic routinely turned to foreign law in making its decisions, something so called originalist Antonin Scalia now decries. For example:
[Justice] Story’s use of English law in American patent cases first appeared just three years after English troops had burned down the Supreme Court’s chamber in the Capitol, along with every government office in Washington except the Patent Office.
This just goes to show that history degrees aren't always useless.