It is not legal to ship alcohol through the mail across state or national lines unless you have a license. That said, there are a variety of ways to ship alcohol (both legal and illegal) that people regularly put into practice. As long as you're not shipping large amounts of alcohol from one point to another, the punishment for getting caught is little more then you losing the bottle or bottles you are sending. In other words, there is a risk in breaking the rules but not a criminal one.
FedEx or UPS, not USPS
The USPS strictly bans the shipment of alcohol and will most likely confiscate your package if they suspect that's what you are shipping. FedEx and UPS don't ban it expressly, but they will definitely make it difficult for you if they think you are shipping it. In other words, don't tell them or give them any reason to suspect you are shipping bottles of booze. Plus, you can track it with FedEx/UPS, not USPS. If you are shipping overseas, this may get harder as many packages are scanned these days when they enter a country to make sure they don't contain bombs or drugs (or illicitly sent bottles of booze).
Packing is Key
Get a big box that is totally nonalcohol related and put large amounts of padding between each bottle. Wrap it in bubble wrap and paper maybe, or a towel or small blanket to pad a couple of them together, so they don't clink against each other when being tossed from one delivery truck to the next. Also, make sure your box isn't going to split open, and that it is sturdy but not too heavy, as this will impede the ease at which it is moved.
Have a Liquor Distributor Send It
Many states have state-run liquor stores or are licensed to ship alcohol for you--each state has its own places, which can be found online. For a little extra money on top of shipping, you can have them send the alcohol and save yourself the personal trouble and fear of breaking the law and losing what you bought. This may be the best option, as it ensures your package will arrive without being lost or confiscated, and you won't be running any risk whatsoever though it seems fewer and fewer people are doing it this way.