In my view, dates and times should be handled as two separate input boxes for it to be most usable and efficient for the user to input. Let the user input one thing at a time is a good principle, imho.
I use the core UI DatePicker, and the following time picker.
This one is inspired by the one Google Calendar uses:
jQuery timePicker:
examples: http://labs.perifer.se/timedatepicker/
project on github: https://github.com/perifer/timePicker
I found it to be the best among all of the alternatives. User can input fast, it looks clean, is simple, and allows user to input specific times down to the minute.
PS:
In my view: sliders (used by some alternative time pickers) take too many clicks and require mouse precision from the user (which makes input slower).
