TL;DR in BLUE

Why this post?
A cursory search of the forums turned up nothing particularly useful on the subject. I apologize if this is duplicate content.This is a really common question though, and I'm really tired of answering this question in detail every time a new player asks me about it.

What is it?
Torn City Time is strange, because the fictional setting for Torn is somewhere in or near Texas, within the United States of America, but it's headquarters' physical location in the real world, and thus timezone, is in Europe. This means the timezone of the servers is Greenwich Mean Time. This time zone is also variously known as Zulu, for some in the military, or Coordinated Universal Time, for nearly everyone else in the English speaking world. Oddly, due to differences in English vs French, the two "lead" languages of the various countries which were party to the treaty that created Coordinated Universal Time, this standard is abbreviated, "UTC". If it wasn't already obvious, you'll also see players here and in various Torn related chat channels refer to it as TCT, or Torn City Time.

Why is it important?
It's important to know what time it is in Torn for a number of reasons.

1) Energy regenerates every 10 minutes on and past the hour.

2) Nerve does so every 5 minutes on/past the hour.

3) Happiness regenerates, or resets to soft cap, every 15 minutes on and past the hour.

4) Points refills(energy, nerve, casino tokens), daily casino tokens, and the spins for "Spin the Wheels" reset every day at midnight, TCT.

5) Companies experience updates or "resets" every day at 6 PM TCT. (This processes slowly, with newer companies likely experiencing updates several minutes past the hour).

6) The lotteries "reset" or draw, every day at approximately 10 AM TCT.

7) Stock Benefit Blocks process every day at midnight, TCT. (This used to process in the same way as Company updates did, but now that the rewards are manually triggered by players each day, I suppose it probably occurs near instantly).
8) Drug addiction naturally "decays" (by 20 'addiction points') every day at 3:30 AM TCT.

 - Note that daily progress toward benefit blocks do not progress toward a recently purchased/acquired increased benefit block unless you sell and reacquire the entire block(resetting current progress for previously held blocks to zero).  It's up to you do calculate whether it's worth losing current progress in order to gain the additional daily progress for a newly acquired block.

If you know of something I'm missing in the above list which is purely clock based and never changes otherwise, please let me know, and I'll include that.

How to determine Torn City Time:
1) If you're travelling, the simple way to see what time it is in Torn City is to open a chat box and say something. The timestamp at the bottom will change to show current TCT(credit to Steven[889354] for reminding me this existed). Also, there are browser plugins for Torn that will display the time in the background among other things. I don't use any of those, so I won't bother linking them here. You can use Google to find them. Another possible solution is to leave another tab open without clicking anything, with Torn's webpage already open from before you started travelling. The clock applet will continue to dutifully count the time as long as the page is not reloaded. Sometimes this even works when you're signed in from another device afterward.
2) On a full size desktop browser(or if you've told your mobile browser to request the desktop version of any particular Torn web page) you'll find the "Torn City Clock", as I like to call it, on the bottom left of the page, just below the column with all of the links to various areas of the city, friends/enemies lists, and the "Specials", which includes a link to your recruitment URL, among other seasonal events.

3) On mobile, or if you're using a very narrow browser window on a desktop device for some reason, it will be directly beneath your status icons, on the left, as shown here:

At some point since I originally posted this, a clock widget has been added to Torn's webpage.  This set of icons is always in the top right now, on all platforms, and I believe all of the desktop clocks mentioned above remain as they were.  The mobile clocks have been removed, and only this one remains(new chat does not even have a timestamp on messages you send, so that's no longer a reliable method).  This is now the most consistent and reliable place to see the current time.  Clicking/tapping it opens it and it will remain open until closed.

That is all.