I'm more than certain that I've seen posts of at least one problem relating to "World Time".
Be that as it may, this is an interesting site: http://www.timeanddate.com/.
Apart from Perplexus I regularly frequent another Forum. I also have a few correspondents (email) around the world. Sometimes I look at a post or email and wonder if there is any immediacy for a reply, or if I can let it slip to "waking hours".
There is a link at the site I think here. My hesitation is that I have set up certain cities around the world and the url of that page point there. Anyway, without too much bother your computer reads the UTC time [still haven't reconciled the subtleties of UTC and GMT], but then, you can have your data applied to an Applet here.
By selecting your "Save" button data is saved somewhere and when you log to your world page (hope you bookmark it), you know at a glance the general status of wakefulness of your chosen parts of the World!
Let's get back to where I opened this discussion, problems relating to World time. I bring this page to attention for its overall usefulness but maybe it suggests something to someone, whether to share an idea or prompt one, for one or more problems ("Around the World in 80 Days").