Rick & Morty do a lot of universe-hopping in their adventures, but they've also had to completely relocate their lives to different universes at least twice over the course of the show. As the Rick & Morty season 3 episode "Morty's Mind Blowers" revealed, the pair have actually erased many of their memories of past adventures, so it's possible that they've change universes even more times than we've seen.
The process of moving universes was first revealed in Rick & Morty season 1, episode 6, "Rick Potion #9." After a love potion designed to make Jessica fall in love with Morty combined with the flu virus, it spread rapidly and caused everyone to fall in love with Morty. Rick's attempt to fix things with subsequent potions resulting in people mutating into horrifying hybrids until eventually they became blobby freaks called Cronenbergs. Unable to figure out how to change everyone back to normal, Rick transported himself and Morty to a universe where their alternate selves had fixed the Cronenberg pandemic and then immediately been killed in a freak explosion.
After burying the dead bodies of their alternate selves in the back yard, Rick and Morty simply assumed their places in a world that was exactly the same as their own (minus the Cronenbergs). This means that technically Morty's family is no longer his actual family, as his real family is still stuck on Cronenberg World - also known as Dimension C-137. At the end of the episode Rick tells a traumatized Morty, "It's not like we can do this every week. We get three or four more of these, tops" - setting up the idea that universe switches are finite, but also laying the groundwork for him and Morty to potentially switch universes several more times over the course of the show.
A second occasion on which Rick and Morty switched realities was revealed in "Morty's Mind Blowers," when Morty recovered a memory of a time when he gained the ability to understand animals and unwittingly stumbled onto the knowledge that major world events were being orchestrated by squirrels. Rick incapacitated the squirrels for just long enough to give himself and Morty time to escape the universe, while also scolding him, "I told you we could only do this a couple of times."
We know with some certainty that Rick and Morty remained in the same dimension between the Cronenberg episode in season 1 and the season 3 premiere, "The Rickshack Rickdemption," because in that episode Morty dug up the dead bodies of his and Rick's alternate selves that they'd buried. The main indication that there are more universe switches we haven't seen yet comes from the difference in Rick's warnings - from saying that they had "three or more" possible universe switches, to saying that they only had "a couple." That could just be Rick's slapdash approach to science, or it could mean that the pair switched universes on other occasions over the course of season 3.
With the arrival of the second half of Rick & Morty season 4 imminent, we could see the pair switch universes again before the year is done - and perhaps even find out why, in a multiverse of infinite possibilities, universe-switching is something that can only be done a few times.
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