As far as I know all mentioned tests are good and reliable (and accepted by journals when you publish). Today Fisher's exact test seems to be preferable especially for smaller sample numbers, with larger sample numbers there is no difference to Chi squared test.
Another test which is highly recommended now is the G-test, which I'd use, if the software offers this one (for R a package is available) and if you have not too small sample numbers (too).
Edited by hobglobin, 15 November 2013 - 09:11 AM.
One must presume that long and short arguments contribute to the same end. - Epicurus
...except casandra's that belong to the funniest, most interesting and imaginative (or over-imaginative?) ones, I suppose.