Eternal Afternoon

 Eternal Afternoon is an indie game where you spend the last 20 minutes of your life doing something before a giant wave comes and destroys all of creation.   

There are plenty of missions and things to accomplish in these last 20 minutes, from writing a love letter to a girl you were too nervous to talk to, finding your lost dad, playing a video game within the video game - and many collectables/achievements.

The game is a long dialog about loss and the end as you encounter various people in your neighborhood, and eventually embrace the inevitable - however the developer added a number of in-game glitches where you can "Kobayashi" the game (the mission Kirk cheated to win IIRC) and escape in some fashion ala Stanley Parable in some cases.

A great idea and well executed.