LaTeX Table Generator
Python 2, 197 bytes

This solution uses string formatting to reduce repetition. Each string component is assembled, then placed within the template. It is tricky to use so many backslashes in Python strings. I used the raw string r'\\' and multi-line '''blah \n blah''' string techniques here.



def a(d,e):
 c='c|'*e;b='&amp; '*e+r'\\';g=' '*4+b+'\n    \\hline\n';f=g*d;h='{tabular}'
 return r'''\begin%s{|c|%s}
    \cline{2-%s}
    \multicolumn{1}{c|}{} %s
    \hline
%s\end%s'''%(h,c,e+1,b,f,h)


Before the minifier, it looks like this:

def latextable(height, width):
    columns = 'c|' * width;
    linespec = '&amp; ' * width + r'\\';
    line = ' '*4 + linespec + '\n    \\hline\n';
    block = line * height;
    mode = '{tabular}'
    return r'''\begin%s{|c|%s}
    \cline{2-%s}
    \multicolumn{1}{c|}{} %s
    \hline
%s\end%s''' % (mode, columns, width+1, linespec, block, mode)

print latextable(1, 1)
print latextable(2, 4)


The output tests:

\begin{tabular}{|c|c|}
    \cline{2-2}
    \multicolumn{1}{c|}{} &amp; \\
    \hline
    &amp; \\
    \hline
\end{tabular}
\begin{tabular}{|c|c|c|c|c|}
    \cline{2-5}
    \multicolumn{1}{c|}{} &amp; &amp; &amp; &amp; \\
    \hline
    &amp; &amp; &amp; &amp; \\
    \hline
    &amp; &amp; &amp; &amp; \\
    \hline
\end{tabular}


As a side note, I wrote a latex macro processor like this to format my thesis. I think I spent longer on developing that macro processor than on writing the words...