What legal recourse does a wife have against the woman who is having an affair with her husband?

None. The only reason the wife has a legal recourse against the husband is that their marriage is a contract, and one which he has presumably violated. Adultery itself is not an illegal act, as I understand it; the crime there is breach of contract. (I suppose it could be argued that the other woman is an accessory to that breach of contract, but I know of no precedent for this.)

Edit: In retrospect, if the affair caused significant trouble to the wife personally (e.g. an expensive divorce), she could always sue the other woman for damages. But that's not a promise or even a suggestion that it might work.

More Edit: I stand corrected, but as can be read in the link behind the comment, the conditions really had to be just right. It would be difficult to prove that quantifiable damage was done.

You have little or no legal recourse against her. Time was, you could sue for "Alienation of Affection", but it now seems to be seen as a relic of a bygone era, and very few states still recognize it. Here's what WorldLaw Direct says about it:

http://www.worldlawdirect.com/article/1026/Alienation_of_affections_--_Law_suits.html

Alienation of affection(s) is a legal action, a tort based on willful and malicious interference with marriage relations by a third party. The elements constituting the cause of action are wrongful conduct of the defendant, plaintiff’s loss of affection or consortium of spouse, and a causal connection between the two. Not all states recognize the right to bring an alienation of affections action. It is usually viewed as not being relevant or easily applied in modern society.

States plus D.C. which have statutorily (i.e. by legislation) abolished alienation of affection:

Alabama
Arizona
Arkansas
California
Colorado
Connecticut
Delaware
District of Columbia
Florida
Georgia
Indiana
Kansas
Maine
Maryland
Massachusetts
Michigan
Minnesota
Montana
Nebraska
Nevada
New Jersey
New York
North Dakota
Oklahoma
Oregon
Pennsylvania
Rhode Island
Tennessee
Texas
Vermont
Virginia
West Virginia
Wisconsin
Wyoming

States which have judicially (i.e. by court ruling) abolished alienation of affection:

Idaho (1986)
Iowa (1981)
Kentucky (1992)
South Carolina (1992)
Washington (1980)

States in which alienation of affection is possibly a viable cause of action:

Hawaii
Illinois
Mississippi
Missouri (appears recently abolished)
New Hampshire
New Mexico
North Carolina
South Dakota
Utah

[To succeed on an alienation claim, the plaintiff often must show that (1) the marriage entailed love between the spouses in some degree; (2) the spousal love was alienated and destroyed; and (3) defendant’s malicious conduct contributed to or caused the loss of affection. It is often not necessary to show that the defendant set out to destroy the marital relationship, but only that he or she intentionally engaged in acts that likely would impact the marriage.]

There are some cases involving transfer of STD from the "other woman" to the wife where the court has allowed the wife who became infected to sue the other woman for negligence when the other woman knew she had the STD, the cheating husband did not know, and it was reasonably foreseeable that the wife might become infected. Also, contrary to another answer to this question, in some states adultry is still legally a felony. However, it is rare to see a district attorney agree to file in such cases.

YES.

The other answers are correct, none. get a divorce attorney. get it done.

Divorce if you want to. Or a restraint order to keep her away.

one free punch directed at her nose

Yep, they are totally right. Divorce... and never look back. I gave my wife chances and she continued her affair harming my daughter and I without the slightest care or hint of remorse. People who do this are completely selfish and always will be.

Don't ever get married again - it's a FARCE! Would you sign any other contract in life that required you to give up all of your rights regardless of everything you put into it? It's a SHAM!!

Take care of yourself and get happy. Living a great life free of the prick is the greatest revenge.

you can discuss the situation with a lawyer, chances are there isn't anything you can legally do to her. It was your husbands choice to do it, and in some states adultery isn't reasonable grounds for divorce. Most of these are handled by stating the marriage is irretrievably broken and that's pretty much it. I'd say, let her have the miserable wretch and let her also have his unfaithfulness. He'll cheat again. It's up to you to see that it's not you he's cheating on. Leopards don't change their spots and she can have a first-hand taste of what she deserves when he does the same to her, and you know he will. Let the whole neighborhood know what she is if it makes you feel better to do so.
Move on and seek happiness with someone who deserves you. Never look back...

UNLESS YOU CAN PROVE THAT SHE HAS SOME SORT OF MIND CONTROL OVER HIM MAYBE BY THE USE OF VOODOO OR SOME OTHER FORM OF MAGIC SPELL YOU MOST LIKELY DONT HAVE ANY RECOURSE. IF HIS HEAD SEAMS TO BE SHRINKING AND HE SPENDS ALOT OF TIME PLAYING DARTS AND ANSWERS TO THE NAME "BYWA ZULU MAKI MAKI" YOU PROBABLY SHOULD FILE FOR DIVORCE

Unfortunately she would probably have to take actions into her own hands. If she has children, then it is best to wait until they are grown, and she might want to wait until she has outlived her parents. Then she should kill both her "husband"/rapist and the woman who was his accomplice. If they are not sorry, then she should make sure they are sorry before she lets them die. If they die without being sorry for what they did, then they could go to Hell forever.

nothing!!! as far as i know, because i have a fiscal friend, you cannot sue the "other woman", why? bec. in the first place, she is not the one who made mistakes with you... or....you can sue your husband for adultery only if... there is strong and enough evidence that he really commited adultery... and what is that evidences: if you found out that they are living-in together and if they are having children, in that case, you have stong evidence of adultery.. then right away, file a case against your husband!!! goodluck!!!

Take her ass to court and put her on public display.

Only one recourse, D-I-V-O-R-C-E!

Against HER? I suppose you could try a lawsuit but I've never heard of one that worked.

Extramarital sex - as long as it's consenting with someone old enough - is perfectly legal.