Fantasy RPGs, like Dungeons & Dragons, present more than a couple options for sleeping. Some of these may include "head on pillow" sleeping, trances, stasis (for mechanical beings), and even consequences for not sleeping. How your character sleeps and where they sleep can be detrimental to their health. In some games, not sleeping will create a state of exhaustion which will affect their ability and saving checks. When your character does sleep, do they sleep on their back or on their side? Maybe they sleep standing up? Or maybe they prefer sleeping in a coffin . . . we're watching you Strahd.
In sci-fi games, like Warhammer 40,000, where increased usage of technology plays a large role, sleep may include stasis chambers, power-saving modes (for mechanical beings), and others. As shown in numerous sci-fi movies, stasis chambers can allow for prolonged space flights, whereas robots and cyborgs will occasionally need to recharge their batteries. Without these sleeping options, the possibility of completing the games' mission may become greatly reduced.
And in horror games, like Call of Cthulhu, the need for sleep may play a huge role in your character's mental health. Discovering certain horrors within your game could begin to make a perfectly sane character drift rather quickly towards becoming a frequent guest in a padded room. A character's sanity can often boil down to if they were able to get a good night's sleep or not. Of course, on the flip side, in some games, sleep might be what drives your character towards purchasing that leather coat where all of the buckles attach in the back.
Happy Sleeping! And may your character find a good night's rest!