There is now the filemod package which can return the file modification date of any file (which can be found by TeX). It is based on the \pdffilemoddate macro. It works with pdf(La)TeX and Lua(La)TeX, but not with Xe(La)TeX.
If you want the time when the main file was last changed use \jobname as filename in the macros below. If you really want the compile time you can
use the macros with a trick:
\edef\pdfilemoddate#1{\pdfcreationdate}
and then keep the {<filename>} argument empty.
You can print, i.e. typeset the date, time and timezone using
\filemodprint{<filename>}
Only the date or time+timezone are printed with
\filemodprintdate{<filename>}
\filemodprinttime{<filename>}
They use the \thefilemoddate and \thefilemodtime to format the result.
These macro get {<YYYY>}{<MM>}{<DD>} or {<HH>}{<mm>}{<SS>}{<TZ>} as arguments, respectively. You can redefine these to print the date or time in a custom format. There is also \thefilemod for \filemodprint which gets all seven arguments and by default calls the other two macros.
You can also create your own macro with seven arguments and use:
\filemodparse{\mymacro}{<filename>}
Then the timezone would be #7.