The heat death of the universe (aka ultimate entropy) is the best of the best arguments as to why human immortality would really suck.

In fact, living through the heat death of the universe (provided you had a habitat where you would not experience the unimaginable torture of living in a vacuum) would be enough to drive any person clinically insane, and then some.

On the other hand, it would be a pretty sweet pick-up line.

"Hey baby, the universe is gonna end in 100 billion years, wanna come back to my place while we still have the chance?"