Is it true that traditionally, Jewish marriages were arranged marriages? I’ve also heard that this is still the practice amongst the more religious Jews. Does Judaism mandate or legitimize this practice?
If arranged means coerced—no. It is true that in most ancient cultures—and many still-existing ones—marriages were and are arranged, and the young lady (and sometimes the young man) has no say in this choice of her/his marriage partner. However, Torah law and Jewish custom have always frowned upon this practice, even in ancient times.
In fact, the opposition to coerced marriages was prevalent in Abraham’s family even before Judaism. We find in the Torah’s account of Isaac’s marriage (Genesis 24) that when Abraham’s servant Eliezer proposes to take Rebecca back to Canaan to marry Isaac, he is told by Rebecca’s family (Abraham’s cousins who were not into his new religion): “Let us ask the maiden.” From here our sages derive that no one may be married against their choice. This, indeed, has always been the practice within the Jewish community since its inception.
As far as how the prospective bride and groom are introduced so that they can decide whether they do indeed wish to marry each other, certainly the shadchan (“matchmaker”) has always played a major role in Jewish marriages. (There are professional shadchanim, but usually it’s a friend of the family who knows someone who knows a seemly candidate, etc.)
The shadchan method has proven to be the most effective way to find a marriage partner. One starts off meeting someone who is at least somewhat compatible, rather than meeting people at random. As a matter of fact, many thoroughly modern Jewish singles have discovered that the random roll-the-dice approach isn’t finding them a mate, and have returned to the traditional shadchan model.