Adding my $0.02 based on my experience checking wine in and out of various countries:

DL, AA and UA have no problems with checking wine in the proper wine shipper box. UA will place a special "blue" baggage tape to indicate that it's a baggage item and not cargo to make sure it ends up on the right flight. In addition, UA may ask you to sign a waiver for fragile item, as it's standard for boxes. However, do not let them tell you to sign for "unsuitably packed" if you are using a shipper box- that waives the liability for breakage. Obviously, this will take up your checked luggage allowance. Although, remember that AA premium cabin passengers can check up to 3 bags, and *G members can also check 3 bags on UA.

For USA customs, the rule is to declare the # of bottles and value. The number of bottles make a difference, since the volume of alcohol imported triggers whether the wine is dutiable or not. Duty is calculated based on the value of the items imported. Personal exemption is 1 liter of alcohol for US residents, which means pretty much 1 bottle. Any excess alcohol is dutied at 3% of value of wine in excess of personal exemption. For example, if you brought a case of wine, at a total value of US$600, you're be responsible for paying duties on $550 (approximately), regardless of the fact that you are allowed $800 exemption as a resident.

However, the CBP agents have been given some latitude of waiving duties. The general guideline seems to be the $800 per person exemption (even though the number of bottles overrides the value), so they can waive duties under $25 or so. You should have receipts supporting the overall value of wine you are declaring, in case they ask (which never happened to me, but you never know). Also, be aware that if you have Global Entry, also declare accordingly, and you'll be sent to an agent instead of instant-clear. Even though some CBP agents have told me that "the wine doesn't matter", if they caught you answering the questions incorrectly, you'll lose your Global Entry privileges.

Also, don't forget to declare all other goods brought into the US.