The issue here is complicated by the fact that \mathbf (the
command for setting bold text in TeX maths) affects a select
few mathematical symbols (the uppercase Greek letters). However
lower-case Greek letters behave differently from upper-case Greek
letters (due to Knuth's esoteric font encoding decisions). However,
\mathbf can't be used even for upper-case Greek letters in
the AMSLaTeX amsmath package, which
disables this font-switching and you must use one of the techniques
outlined below.
The Plain TeX solution does work, in a limited way:
{\boldmath$\theta$}
but \boldmath may not be used in maths mode, so this 'solution'
requires arcana such as:
$... \mbox{\boldmath$\theta$} ...$
which then causes problems in superscripts, etc.
These problems may be addressed by using a bold mathematics package.
\bm which
may be used anywhere in maths mode.
\boldsymbol, which
(though slightly less comprehensive than \bm) covers almost all
common cases.
All these solutions cover all mathematical symbols, not merely Greek letters.