Alienation of affections basically consists of a defendant's (1) wrongfully (2) causing plaintiff (3) to lose the affection and often company of the plaintiff's spouse. In principle, it could apply to supposedly meddling in-laws, and has sometimes been applied that way, though if the in-laws are looking out for their married child's best interest such behavior might not be "wrongful." In practice, it has generally been applied to people who supposedly seduce away one spouse from the other (if it can be shown that they caused the alienation, rather than that a preexisting alienation of the spouses caused one spouse to be interested in the defendant's attentions). The related tort of criminal conversation basically consists of a defendant's having adulterous sex with plaintiff's spouse, though of course such conduct may also often lead to an alienation of affections claim.
Many people assume that these two torts are dead. But some states -- Hawaii, Illinois, Mississippi, New Mexico, North Carolina, South Dakota, and Utah -- still recognize them (or at least recognize the alienation of affections). And it turns out that they still account for a significant amount of litigation, not much less than some well-established torts whose viability no-one doubts.
It seems that the main jurisdiction in which there's a good deal of alienation of affections litigation is North Carolina. My search through the NC-CS and NC-TRIALORDERS databases in Westlaw uncovered 38 cases from 2000 to mid-2009, and it seems likely there were more (since those databases don't offer a complete list even of decided cases, and entirely exclude ones that were filed but were settled before any decision). By way of comparison, the well-established tort of slander (oral defamation) seems to be litigated only slightly more often than alienation of affections in North Carolina. The well-established right of publicity seems to be litigated in North Carolina much less often than alienation of affections (2 cases since 2000 in the NC-CS and NC-TRIALORDERS databases, as opposed to 38 for the alienation of affections).
Even on a national basis, a search for sy("right of publicity" ((misappropriat! appropriat!) +5 (name likeness image))) & date(> 1/1/2000) through the ALLCASES database yielded 150 cases, while sy((alienat! +3 affection) "criminal conversation") & date(> 1/1/2000) yielded 66, of which 50 were in jurisdictions that still recognize one or both of those torts. Now naturally these results may not be representative of all cases litigated through trial, or of all cases filed in court. (For instance, there might be reasons why people might be more or less likely to settle right of publicity cases than they are to settle alienation of affections cases.) Also, my right of publicity query might have excluded some cases in which the matter is discussed solely as "invasion of privacy" (from which the right of publicity derived).
Still, the comparison suggests that alienation of affections claims are not vastly less common than right of publicity claims, which no-one treats as moribund. In many states, it has indeed been abolished, so it's not of practical importance to lawyers who litigate solely under the law of those states (though even California lawyers might come across it if, for instance, their clients acted tortiously in North Carolina, or perhaps even in California with a visiting North Carolinian). But I think it should still be seen as being of scholarly and pedagogical significance to tort scholars and teachers, untainted by a sense that it is somehow entirely moribund.