This really depends on the barn you board at, and you should know your barn owner/staff's reaction to people leaving, having probably seen other people leave. At my barn, people come and go for different reasons.....sometimes seasonal, training reasons, or they think they found a better deal. Our barn owner would never intentionally burn bridges with people, because oftentimes they come back.
We did have this one lady who gave a month's notice and got really paranoid. She started asking people to keep an eye out for her horse to make sure he wasn't neglected during that last month. Seriously? At a big barn, people come and go. This lady had been there long enough to know that our BO would *never* mistreat a horse because the owner wanted to move.
I have heard of some really looney barn owners where you would want to maybe spend the extra money to pay for that month or several weeks in advance and, as the op said, get the heck out of there one day. So long as you have paid for that month and that gives them time to find a new boarder, that is fair. I wouldn't expect to go back to that barn any time soon though...lol