They can be done through a grand battle like the destruction of the Death Star in Star Wars or can even be a conflict of wits and unfolding plans like in Death Note or A Most Wanted Man.
But game stories have always had a preference for combat to keep the player interested, involved and empowered. In fact it's rather hard to think of many games with stories to tell that don't have combat of some sort in them.
When done wrong....
Keep in mind that these are all by modern-day standards. I'm sure defeating Bowser by removing the bridge from underneath him was amazing or iconic back in the day, but this is 2015. We have better.