For a few years it was standard procedure. It was accidentally discovered when the Enterprise was falling into a collapsing planet. Cold starting the warp drive took them three days into the past. And you know, saved everyone's life.
Using that as the basis, the slingshot effect was used to study the past until it was deemed too dangerous to use regularly.
In 2286, the effect was used to bring the humpback whale from the 1980s, in order to prevent an ancient probe that had come in search of whales from terraforming Earth.
As far as I know, it's never been used to hop universes.