'Tis true, there are lots of passages in the Old Testament that seem to be not relevant to today's society. Personally, I don't get much edification from all the begats, and yet I think it's important to remember that our past is part of who we are--and that includes all those saints and not-so saintly saints listed in the begats. However, it is the commands that trip us up when we read the Old Testament, commands like not boiling a kid in its mother's milk; just how do we make such a command relevant to today?
This particular command is found in three places in the Old Testament: Exodus 23:19, 34:26 and Deuteronomy 14:21. In each case it is found either at the end or the beginning of a listing of commands regarding tithing, and in the Deuteronomy passage it falls at the end of a list of purity laws. Because of this particular scheme it has been conjectured that this phrase may be either a subject marker, a passage divider, or a subtle reminder of the purity laws to the Israelite reader. It may indeed be any or all of these, however this doesn't change the fact that we must deal with the phrase itself.
Of the three occurrences of the phrase, only in Deuteronomy is it found in a context that "makes sense." In Deuteronomy the prohibition falls as the last in a list of dietary laws for the Israelites. These laws became the basis for the kosher dietary laws kept even today by orthodox Jews. This particular law, not boiling a kid in its mother's milk, is the only dairy law in the list. This law today has been expanded to cover the prohibition of preparing meat with any milk product. For instance, a cheeseburger or pepperoni and cheese pizza are both forbidden by the kosher laws; this because of the possibility of eating meat with a milk product from its own mother.
So if you want to remain kosher even today, this law is still applicable. But what about the Christian who has chosen to be exempt from the kosher laws (as nearly all have chosen)? How is this verse relevant? Again, the burden is on the reader to interpret the passage into today's society. It seems clear that the basis for the law in the first place is one that prohibits wanton cruelty even (or especially) to animals. There is indeed something that seems particularly insidious when one contemplates, for instance, cooking veal in the milk from its own mother. Indeed, my understanding is it is still a delicacy of the Bedouin tribes in the Middle East to eat a kid boiled in milk from its own mother. For those who have not been at a dairy farm and seen the distress of a mother separated from its calf, know that the separation process can be heart-wrenching. To add injury to insult by cooking the animal in its own mother's milk seems abhorrent.
But the parallels need not end there. Any cruel act can be measured against this verse, for instance the "harvesting" of infant seals for their fur, the closed quarters used to raise a calf for veal, and the boiling alive of crustaceans to name a few. Cruelty has never been condoned in the Bible, New or Old Testaments, and this verse is relevant today, if only to remind of this fact.