Recently, in fact.
In my D20 game (see link in sig), the PCs have a TARDIS. They arrive at a secret Antarctic research base to rescue one of their own, only to find the base utterly destroyed. No bodies remain. Evidence points to an assault by lots of badass things--all the bullet holes in the buildings are from the inside out.
Well, of course they decide that the only way to save their buddy is to travel back to before this destruction occurred. And no problem, the
unknown past can be altered. It's the historical certainties that won't be altered. So while they may be able to save their friend, they realize that there's no way to prevent Zero Station being destroyed. They saw it in ruins: its destruction is a certainty.
So they travel back six days or so. Manage to save the companion. Blow up a little of the base. Interact with the base crew a bit from the safety of their (camouflaged) TARDIS. But, there's a wrinkle: the TARDIS sensors detect a quantum singularity only 181 miles away.
They could leave at this point. But they're curious. Hell, they're terrified. Why is there a black hole on Earth?
So they drop off their rescued buddy at home, and travel to the coordinates of the singularity. There they find a massive stone obelisk/tower. The tower is only the tip of a massive and rapidly-failing construct designed to keep an enormous extradimensional horror inside, run by Lovecraftian Elder Things.
They talk to the Elder Things (those whose minds are up to it at that point), and discover that a tiny bit of the enormous extradimensional horror has escaped into their TARDIS, and is now feeding on the artron energies found in the engine room. They're about to rush out and capture it, when the Elder Thing asks whether there are more pieces of said enormous extradimensional horror at the research base.
"Yes, there's one," they reply.
And are the humans experimenting on my people?
One PC is shaking his head, whispering "Don't tell them..." They know full well that the base crew is performing creative autopsies on the remains of at least half-a-dozen Elder Things. Then they tell the Elder Things so.
Elder Things, of course, freak out.
As they flee the tower, hundreds of Elder Things come flying out of it, into the sky, headed toward the base. Checking the calendar, they realize that this is about the time the attack must have occurred.
...And that they caused it. (see sig link for lots more detail.)
Never have I had a time-loop scenario work out more perfectly. I think the fact that it "just happened," rather than being designed, was the reason it worked so well. Didn't feel forced at all, but it did feel like fate. Fine line.
So my advice is to just let it happen on its own...but it can't happen at all until you give your PCs a time machine.
Henry said:
...some DM's resort to finicky time gates, plot devices out of the players' control, etc. In order to inject time travel, but without it becoming a big mess.
We use the online
TARDIS manual. It's treatment of the Whovian "Laws of Time" was perfect for keeping things fun, but within limits.