Companions and great voice actors are another important tool in making a decent game, into an epic game. While some people might undervalue this aspect in comparison to graphics and other areas of gaming, it does play an essential role in drawing people into their world. By having unique and interesting companions with you, makes you look forward to every piece of dialogue or conversation in the game, it makes you want to learn more about them and in doing so learn more about the world around you. Having characters that act like your wing (wo)man just generally makes you want to play the game just that little bit longer, especially if you're able to level them up and watch them gain new abilities.
But what would really take games to a whole new level of amazing, would be to see games break the restrictions on romance options, get rid of companions that give long tedious explanations about their lives, give companions actual dialogue that relates to each main quest so that you can engage them throughout the game, design companion side quests that will have a genuine impact on the results of the main quest, and be able to befriend anyone you meet on the road, not just companions you have to use because they're part of some main quest or side quest. I think by doing all that, games could become a lot more immersive.
Lastly having voice actors that are good at what they do, by conveying emotion through their voices or bringing the characters words to life can play an important role as well. A good example of this is Ezio in Assassin's Creed Series, his voice is constantly being adapted to show his age and his maturity. Now while you might not be able to notice the subtle difference, the way it gets deeper and gritter in each Ezio game in the series does affect the way you perceive your character.