If you are doing what I believe you are trying to do, you’ll need something a little more like this:
table {
border-collapse: collapse;
}
table td, table th {
border: 1px solid black;
}
table tr:first-child th {
border-top: 0;
}
table tr:last-child td {
border-bottom: 0;
}
table tr td:first-child,
table tr th:first-child {
border-left: 0;
}
table tr td:last-child,
table tr th:last-child {
border-right: 0;
}
jsFiddle Demo
The problem is that you are setting a ‘full border’ around all the cells, which make it appear as if you have a border around the entire table.
EDIT: A little more info on those pseudo-classes can be found on quirksmode, and, as to be expected, you are pretty much S.O.L. in terms of IE support.