Synchronize with the correct time This may not be Drupal specific, but does Drupal have a module that can fetch the correct world time from any remote time server, which can help me in keeping the time shown in my Drupal site correct?

I don't want to use my system time which may be inaccurate.
If you are on shared hosting your hosting company should be responsible for keeping the time correct. If that's not happening contact them and ask why. If you are on VPS or your own private server you can set up a NTP client as tostinni recommended.