There are quite a few instances of this happening in Doctor Who and some of its spin-offs. Examples off the top of my head:
* For almost all of the Second Doctor's era, he was travelling with Jamie - who came from 1746 (and for one of his seasons he was also travelling with a Victoria - who was a Victorian), so stories like The Web of Fear or The Invasion with contemporary settings (i.e. 1960s) would be examples. There's also a second Doctor novel Invasion of the Cat-People where companions from the 60s (Ben and Polly) encounter the 90s. The passages focusing on this are pretty much the only good things in the book.
* One of the main guest characters in fifth Doctor story The Awakening is from 1643, though the story is set in the then-contemporary 1980s.
* There's a series of fifth Doctor audios where one of the companions is Egyptian Pharaoh Erimem, and I'm pretty sure some of them have a modern day setting.
* Seventh Doctor story Ghost Light is set in the Victorian era, but one of the characters is a neanderthal who had been placed in suspended animation.
* Ninth Doctor novel Only Human has a subplot where a neanderthal settles in then-contemporary 2005.
* Torchwood episode Out of Time is about three people from the early 20th century who are displaced to the early 21st, and how they cope with the change. It's pretty much a perfect example of the basic idea, and is easily one of the best episodes of the series.
There are almost certainly a dozen or so other examples that don't immediately come to mind, as you'd expect from such a long-running time-travel show/franchise.