ConTEXt doesn't seem to typeset quotation marks correctly

The standard font set up in ConTeXt (MkIV) doesn't activate the 'standard' TeX ligatures for quote marks. Instead, the ConTeXt approach is to use logical mark-up here

\starttext
\quote{Hello world}
\stoptext

Note that the ligatures -- (en-dash) and --- (em-dash) are activated as these two are generally useful.

Whilst it is possible to load fonts with different ligature set ups, as this approach is a deliberate decision by the ConTeXt team I would recommend using the \quote macro. (See http://www.mail-archive.com/[email protected]/msg25342.html for discussion about ligatures in ConTeXt.)

In addition to Joseph's answer, the other way to use quotes is to input unicode quotation marks:

\starttext
“How do you ‘like’ those?” said the horse.
\stoptext

You can set shortcuts in your editor to typeset the quotes quickly. For example, in vim, one can use the digraphs CTRL-K+"+6 for open double quote and CTRL-K+"+9 for close double quote and CTRL-K+'+6 for open single quote and CTRL-K+'+9 for close single quote

As mentioned by egreg, on Mac you can type ALT-{ and ALT-SHIFT-{ for double quotes and ALT-} and ALT-SHIFT-} for single quotes.