Videogames started as something simple, with games like Pong and Tetris being purely about their gameplay. Nowadays, a story is a critical component to keeping players interested and engaged. There are a variety of ways to tell stories within video games with cutscenes being the most popular. However, newer games are utilizing in game events to tell stories in powerful ways.
The biggest thing that developers miss is the emotional connection. Before you tell a story about a powerful wizard who can change the world, you have to make your audience care about the character. Perhaps he is an orphan, or he is trying to save his sister. Creating emotional ties will keep the player far more interested than letting them have superpowers with no recourse.
Another common mistake developers make is creating a story that has nothing to do with the gameplay. Come up with a concept for how your game will be played and develop a story from there. It doesn’t make sense to make a story and then a game, because it’s a game after all.
Modern examples of great games to look for inspiration are Half-Life 2 and Portal. These two gems both use story to great effect to create compelling situations and characters.