[Edit: Sorry, I was in a hurry and slaughtered this answer. I wanted to just give a reply in case no one else did, but bungled it. There's detailed replies to the above answer the better spell out that they can't regulate what someone does in a different state. I suggest reading the other responses to better understand this, and ignoring this one. I'll leave it just so you can see how not to respond in a hurry.]
In general, it's not illegal and is the basis behind the states rights movement.
It's been an ongoing thing in the US, probably forever. I think Louisiana still had a legal drinking age of 18 until the mid-80s when they finally changed it to 21 -- only because Reagan was going to withhold federal money from the state. People still have to drive to wet counties/states if they live in a dry one (eg. no alcohol can be sold).
There are some things where crossing the border and doing something can get you in trouble, like trafficking or reselling certain things.