For me it depends. A game with a great story will keep me into it, and with those I usually finish. What keeps me into it, however, is the characters. Companions, side characters, villains, just people you spend the majority of the game with. The characters are why I go back to Dragon Age: Origins, why I've beaten it 18 times and bought five copies of the game over the past few years. It's also part of why I've beat Dragon Age 2 a combined total of two times.
The final thing for me is gameplay. Which is, again, why DAO was WAY more fun for me than DA2. It's why I found Saint's Row: The Third more interesting than #2, and why I loved Mass Effect 3 more than 2.
All and all, how long I give a game to impress me varies. If it's a huge open world game, or an RPG, I give it about 6 hours. If it's a shooter it gets an hour.
(Note: There are exceptions to my opinions, take Wasteland 2 for example. Companion characters really suck and the story is fairly mediocre, but the universe and tone in it is enough for me to come back to time after time)
The final thing for me is gameplay. Which is, again, why DAO was WAY more fun for me than DA2. It's why I found Saint's Row: The Third more interesting than #2, and why I loved Mass Effect 3 more than 2.
All and all, how long I give a game to impress me varies. If it's a huge open world game, or an RPG, I give it about 6 hours. If it's a shooter it gets an hour.
(Note: There are exceptions to my opinions, take Wasteland 2 for example. Companion characters really suck and the story is fairly mediocre, but the universe and tone in it is enough for me to come back to time after time)