\begin{tabular}{|l|l|l|}
\hline
Column A & Column B \\
\begin{math}
x & y \\
\end{math}
\end{tabular}
This won't let me compile and gives a lot of errors, how do I enable math mode in a table without using $ on everything?
\documentclass{article}
\usepackage{amstext} % for \text macro
\usepackage{array} % for \newcolumntype macro
\newcolumntype{L}{>{$}l<{$}} % math-mode version of "l" column type
\begin{document}
\begin{tabular}{| L | L |}
\hline
\text{Column A} & \text{Column B} \\
x & y \\
\end{tabular}
\end{document}

tabular that a special column specification follows.
\text, you can use \multicolumn, too.
If most of the table consists of math-mode material, it's preferable to use an array environment instead of a tabular environment. Any text-mode material in the table can be handled by encasing it in \text directives (requires the amsmath or the amstext package):
\documentclass{article}
\usepackage{amsmath} % for "\text" macro
\begin{document}
$\begin{array}{|c|c|}
\hline
\text{Column A} & \text{Column B} \\
x+y & x-y \\
\hline
\end{array}$
\end{document}
\text directives to typeset the column headers. As you can probably guess, the argument of \text is typeset in text mode, not math mode. The material in the argument of \caption is typeset in text mode by default.
If you use tabu, it automatically detects whether the table is in math mode, thus imitating this feature of array.
\documentclass{article}
\usepackage{amsmath,tabu}
\begin{document}
$\begin{tabu}{|l|l|}\hline
\text{Column A} & \text{Column B} \\
x & y
\end{tabu}$
\end{document}

arrayenvironment (while in math-mode, obviously) instead of thetabularenvironment. If it's just the occasional column that's supposed to be in math mode, you could change its column type specifier from, say,cto>{$}c<{$}.\text{Column A}to switch to text mode in the column headings.$ ... $is a short form for\begin{math} ... \end{math}, so using the latter is unnecessary verbose.arraypackage to be able to use the advanced column specification thingy (e.g.>{$}c<{$}).