Using Bootstrap 3.2.0 I had problem with Brett Henderson solution (borders were always there), so I improved it:
HTML
<table class="table table-borderless">
CSS
.table-borderless > tbody > tr > td,
.table-borderless > tbody > tr > th,
.table-borderless > tfoot > tr > td,
.table-borderless > tfoot > tr > th,
.table-borderless > thead > tr > td,
.table-borderless > thead > tr > th {
border: none;
}