Sadly the human mind is not capable of grasping the concept very well, let alone dealing with the effects of it. The biggest being that we are emotional based creatures, and this leads to a constant stream of pain and suffering, eventually capitulating in a hellish existence once the prospect of death is removed from the table. It is just not in our nature to be able to think on true immortality past the 'oh my god, it would be cool, I could swim in lava and not be deaded!' Swimming in lava... gets boring fast, particularly when you find yourself stuck at the center of the earth.
It is for this reason that beings which are timeless, let alone immortal, are sociopaths at the very least. Their brains are wired not to feel emotions, not to make all but softest of links with each other, just so they will be shielded from the misery that comes with out living all those around themselves. Even the ones that make emotional connections, normally to other timeless beings, are wired so differently from us that we can not fathom how they think. They are that alien, normally very beautiful but so very alien.
Addams wrote about it, and that man was far greater then I.
As for humans whom find themselves with immortality? They tend to take it either of two ways. First lot go through several different levels of insanity before focusing on brief moments of pleasure without a care for anyone else, developing a few layers of shielding to protect themselves. The second undertake mind boggling 'quests' that can never be completed, just so they have something other then sinking into endless depression.
Example of the later is from Addams work, the guy who dedicated his life to insulting every single person... ever! Not just those he came across in his life, but to actively seek everyone to ever be born and insult them at least once. As for the former, Jack Harkness springs to mind as that guy is so cold and yet so hot at the same time. He had no qualms about sacrificing kids, even the child of someone he loved and whom saw him as a uncle, without even a moment of hesitation.
The human brain is just not meant to be timeless, let alone immortal.