There are certain contingencies that the idea of "living forever" kind of ignores when being discussed generally/casually. For example, getting off of Earth and finding another place suitable to sustain human life - what if that never becomes a reality before the world is destroyed? You'd be destroyed along with it. So even "living forever" isn't necessarily attainable without various types of refreshment.
But, assuming one could eventually get off the Earth before ultimate destruction, personally, I think I could do living forever. You'd have infinite time (literally) to figure things out, study the universe, maybe be the one who gets out there. People keep mentioning repetition, but that old saying about change being the only constant is pretty much true when you look at how the universe operates. There would always be new things to discover, new things cropping up, as old things were destroyed. Shifting of culture, new people, new life-forms. you'd get to see life evolve as no human being has ever gotten to. You'd come to know the limits (if there are any) to the various forms of life possible/plausible. Imagine an eternity of experimenting in plant husbandry, breeding Venus fly traps under various survival pressures, trying to create a Little Shop of Horrors. Think of the breadth of mechanical/chemical/electrical/medical/etc. knowledge you could amass, very possibly coming to conclusions about pairings of various methods and technologies that no one has ever come to because they specifically couldn't see that "big picture" you would have. There would always be new things to see and new things to try. And there would always be other life-forms surprising you with new culture and twists on old favorites - because no one, no matter how much knowledge they have, has infinite imagination. And if you ever came to a point that you felt there weren't anything "new enough", you'd have your choice millions of lovely places you'd know to settle down and relax for a nice long while - and any number of other types of beings to interact with. Imagine knowing, for certain, that you had absolutely no responsibilities to attend to, no deadlines to meet.
Besides... if it really got as bad as everyone assumes it would, you just let yourself die with the next planet that sees its end, or chart a course into the nearest star. Yeah... I think I could handle it. No problem.