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).
In the default configuration, lower-case Greek letters behave differently from upper-case Greek letters (the lower-case greek letters are in the maths fonts, while the upper-case letters are in the original (OT1-encoded) text fonts).
The Plain TeX solution does work, in a limited way; you set a maths style, before you start an equation; thus
{\boldmath$\theta$}
does the job, but \boldmath may not be used in maths mode. As a
result, this solution requires that you embed single bold characters
in a text box:
$... \mbox{\boldmath$\theta$} ...$
which then causes problems in superscripts, etc. With
amsmath loaded,
$... \text{\boldmath$\theta$} ...$
does the trick (and is less bad in regard to superscripts, etc), but
is an unsatisfactory solution, too.
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 apply to all mathematical symbols, not merely Greek letters.
This answer last edited: 2013-06-12
This question on the Web: http://www.tex.ac.uk/cgi-bin/texfaq2html?label=boldgreek