Suspended animation makes various appearances in Star Trek. It's a great concept that would solve certain problems in sub-light travel (TOS "Space Seed") or give an individual a one-way trip to the future (TNG "The Neutral Zone", VOY "The 37's"). "Space Seed" portrayed a hibernation process that drastically slowed all bodily functions, while the two later cases were about cryonic freezing that stops everything. The opening scene of Genesis II (1973) is among the coolest things Roddenberry ever did. The hero's body is in a hibernation chamber that got buried in an earthquake and lost for centuries. Then he is found and revived. That really stirs the imagination. In real life, the remains of some dead people are frozen, but as you might surmise from the way I framed this sentence, I don't think they're ever coming back. They don't get frozen soon enough after dying, and there are other obstacles too, as described in the Wikipedia entry for Cryonics. It looks pretty bad. Reversible hibernation, on the other hand, has been limited to cases of very short duration but it seems like the more plausible route. I personally wouldn't volunteer for an experiment, but I can envision progress coming. I think waking up in a future era is a good sci-fi concept, but the reality is too full of unknowns to try it out.
Two of my favorite suspended animation stories are Heinlein's THE DOOR INTO SUMMER and van Vogt's "Far Centaurus." SUMMER is a tour of many technological marvels, some of which have already come to pass. "Centaurus" is the ultimate bummer for long-duration spaceflight travelers. A favorite scene is when one of the sleepers temporarily awakes on schedule partway through the voyage to witness an unidentified bulk in space burning with iridescent fire. The Wikipedia article noted above mentions Benjamin Franklin: I did not know of that letter, which gives sudden relevance to Halperin's THE FIRST IMMORTAL, a near-future novel about suspended animation with a main character named Benjamin Franklin Smith.
I wasn't aware of that Franklin letter either. It's kind of funny to me because after I read his autobiography, I found myself often imagining that I had a thawed-out Benjamin Franklin as my traveling companion, and I was showing him the modern world. I think he should have asked for at least 200 years in the freezer so we could show him better stuff than railroads and the telegraph.
If we could figure out how tardigrades do their thing, we might genetically modify a type of human suited to long-duration spaceflight. Homo freezdrydus. Can survive on very little food, does not need a spacesuit, and can tolerate the raw sunlight from any star. "C'mon, hit me as hard as you can."
We all know of real examples in nature of certain species that are literally frozen for a period of time and then are revived or re-animated back to life with no harm done. For example some frogs and certain fish do this. There are also bears and others that hibernate which is essentially metabolism slowed way down for a period of time and then almost like clock work their systems start to reawken, so to speak. Experiments have been done with certain animals like mice, pigs and dogs where the body temperature was lowered to a set level (not freezing) and a solution injected into the blood stream that did induce a form of hibernation. Later the solution was flushed from the system and the body temperature raised to normal and the animals revived with no apparent ill effect. These experiments were done with the idea of helping victims of trauma in serious accidents---the idea being with the bodily systems slowed down there is more time to get the patient to better facilities to treat them. But the implications of the idea---if it ever works successfully with humans---could be far-reaching in terms of interplanetary and interstellar spaceflight. If the crew is basically asleep then you can save a great deal of energy and resources during the flight. The whole ship doesn't have to be sustaining a habitable environment in-flight if everyone is hibernating in a capsule of some kind. You also don't have to sustain people (food and drink) and keep them occupied (in the conventional sense) when they're asleep. That said you would need a monitoring system capable of intervention if something goes wrong. You'd have to be able to wake the crew or certain individuals early if an in-flight emergency arises. It's possible the crew could sleep in shifts so that someone is always awake or immediately available in-flight.