Styling the last td in a table with css

You can use relative rules:

table td + td + td + td + td {
  border: none;
}

This only works if the number of columns isn't determined at runtime.

The :last-child selector should do it, but it's not supported in any version of IE.

I'm afraid you have no choice but to use a class.

You can use the :last-of-type pseudo-class:

tr > td:last-of-type {
    /* styling here */
}

See the MDN for more info and compatibility with the different browsers.
Check out the W3C CSS guidelines for more info.

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