I don't know why you'd ship actual live beings across interstellar distances. Either implies there's a way around the speed of light, or somebody is really fucking bored. The later is of course more likely.
I can see it for the closest star systems to ours, the dozen or so stars within about 10 light years of the Sun. If we can get a spacecraft to 90% of the speed of light, time dilation cuts the elapsed time aboard the ship down to 43 percent of the elapsed time on Earth. The crew would perceive getting to Alpha Centauri in just 1.84 years.
I really recommend watching Scavengers Reign for anyone who finds this type of thing interesting! I guess it's probably not scientifically accurate from a speculative evolution point of view, but wow the level of thought and detail put into the alien ecosystem is mind blowing. Really beautiful show.