FTL travel is the most common in most stories, though there is generally little attempt to justify the actual method used. An exception to this are the novels by David Weber, where he postulates varying levels of hyperspace, each smaller than the previous but all mapped to a point in real space so travelling in a higher band allows you to travel faster in real space terms. In her Vorkosigan books, Lois Bujold allows travel between solar systems via wormholes so the ships bypass much of the apparent distances between the stars. However, only stars that are on the wormhole nexus can be visited, making those nexus points military and trade choke points. An interesting variation on the distance problem was Robert A. Heinlein’s solution in Starman Jones
. In this novel, the apparent distances between the stars was a form of illusion and getting from star to star was just a matter of exiting the start point at the correct angle for your destination point. Even Heinlein did not use this method
of travel outside this book. E. E. 'Doc' Smith's
spaceships in the Lensmen books did not worry about the light speed barrier at all; with the complete neutralisation of inertia via the Bergenholms, the only limit to a ship’s speed was the heat generated by friction against the interstellar medium and effectively allowing FTL travel without leaving our universe. This interstellar medium is the reason why that standby of the ‘No FTL’ crowd’s favourite, the interstellar Ramscoop, has suffered a near fatal loss of credibility. The Ramscoop looks good at first sight. All it is, very basically, is a life module and a fusion reactor stuck at opposite ends of a great long tube. There is no need for vast supplies of fuel as massive electromagnetic fields are extended forward of the ship that act as a guide for the interstellar medium to be fed into the reactor, where it is used as propellant material. However, current figures on the density of the interstellar medium indicate that it is much denser than first thought, meaning that the scoop would be choked, and at any meaningful speed this compression would provide a lethally high level of radiation. Robert Heinlein (again!) had a fleet of Ramscoops beginning to explore the Galaxy in Time for the Stars
. Of the STL ship types still in contention as it were, the sleeper ship is the most eerie. In this type of ship, the vast majority of those aboard will have been frozen in some form of suspended animation. This usually involves reducing their core body temperatures as near to zero as possible so that life signs are slowed as much as possible. However, as experiments have shown, it has proven very difficult to reduce the temperature fast enough to stop dangerously large ice crystals forming in the smaller blood vessels of the vict… er, volunteer leading to mushed brain! This was a plot point in the Barnes, Niven, and Pournelle Heoret books where all the First Colonists suffered from some of brain damage.
Multi generation interstellar travel has been another staple of Science Fiction from the relatively early days. Basically what you do is either build a great big massive ship, or convert a spare asteroid, so that they can hold a sufficiently large crew and passengers so that they can maintain a population over hundreds, or thousands, of years. Most stories that have used this method of travel have concentrated on what happened after the inhabitants had forgotten they were aboard a ship. The reason for this could be as simple as the length of the journey being so long that the ship has become The World and any thought of an Outside is simply Unthinkable. Other common disasters include a rebellion of the crew/passengers destroying the records of their origins. Heinlein’s, (why spoil a run?), Orphans of the Sky is one of these. Brian Aldiss’ Non-Stop had the crew of the ship rebelling against their officers and a disease ripping through all Earth based life forms on its way home.
A rather interesting drive that appears to have had fairly limited coverage during the seventies was the Improbability Drive, probably most famously in Douglas Adams's " Heart of Gold" in The Hitchhiker’s Guide to the Galaxy. The scientific justification for this is based on Heisenberg’s Uncertainty Principle, which (very) simply says there is no definite way of saying that an atom is in a particular place. Rather than having fixed orbits, the electrons are contained in a shell, which is most dense where they are most likely to be, but with a curve that allows for the possibility they are light years away from the nucleus. The probability drives are able to fiddle the curve so that the ship appears there rather than here.