One reason why games attract me is the possibility to do things that would be incredible difficulty to do in real life by lack of money, proper time and zombie outbreaks or that would be in fact impossible, like powerful magic, fighting huge monsters and zombie outbreaks. The fact that games allow me to do things otherwise I couldn't do is one of the best things unique to games. It is one of the things that no other form of media can give you.
The feeling of power.
Maybe because of my background, I always feel one of the coolest things is when a character do something incredible, even if not realistic. I grew up with lots of Japanese shows, like Super Sentai, Kamen Rider and anime. One of my favorite shows had a ship the size of a city punching another ship almost the same size, then firing thousands of missiles inside it. You may have heard of it. It is called Macross/Robotech.
Because fuck you.
Therefore, every time I can make the on-screen character do something incredible awesome, I have all those nice feelings inside me. Take Final Fantasy and their summons. I know they are just fancy magic, but the sensation of summoning a huge dragon who blow up your enemies with incredible explosions is unparalleled. Plenty of games still give you this incredible sense of power, despite many trying to do some pseudo-realistic settings. One of the coolest things to do in games like Bioshock is to zap a bolt of electricity in your enemies and then blow then up with an overpowered steam punk rocket launcher. Or to take a car in Burnout Paradise, do a barrel roll, take out some other car and then make a mile long jump. This is something that only games can give you.
Making the player feel like he is awesome isn't an easy task. After all, games have their limitations. It is not easy to take in count all the player may want to do. Also, you cannot give full power to the player or you risk taking away the challenge of the game. And if you can use the superpowers easily, you cheapen the reward of doing something really amazing. A special attack, powerful magic or really fucking big gun must be a reward in itself, making you feel like there is nothing you can't do.
Doing this was awesome every fucking time. DIVINE ASSAULT!
The combination of factors to make the player feel powerful is simple and difficulty to accomplish. It must require skill, it must be flashy, and it must result in awesome and significative consequences. A power that is just smoke and mirrors and cause no real effect on the game will feel time lost and that is ripping off the player. Meanwhile, a visually unimpressive but useful and powerful move will not feel as satisfying when you pull it off.
Being able to do something really impressive is some of the greatest rewards I can have playing a game. A mile-long sniper shot. Taking down an enemy fighter jet doing a cool maneuver. Exploding an enemy in a great ball of fire. All of that are reasons to make you smile when playing a game and something that only games can give you.
Give me power, so I can feel like the most awesome human being on the planet.
Too late to take it back. BWAHAHAHAHAHA!