While the cloak is almost a character in and of itself in the film, that doesn't mean it isn’t interesting in the comics. The cloak is a major part of Strange's skill set and was passed to him from the Ancient One. The cloak responds to the commands of its owner even when they're not around wearing it. It can ensnare opponents, offers protection from various attacks, and can alter its shape. But its main draw, of course, is that it lets the wearer fly up to speeds of 25mph.
Strange's amulet isn't just for show
The Doctor's go-to neckpiece, the Eye of Agamotto, has been in comics since 1965. While the amulet helps Strange toy around with time in the movie, its power has been far more diverse in the past, known to transport multiple beings through space-time to any given point in the universe, and also work as an all-revealing light that allows Strange to see through disguises and illusions. In some comics, the Eye of Agamotto's energy has been strong enough to levitate someone as heavy as the Hulk with minimal effort from Strange. The light the eye gives off can also weaken evil beings from demons to the undead. And yes, it can play back recent events.