You should be worried about far smaller numbers that relate to the explosion of the sun, and the heat death of the universe.
EDIT: Sorry, I just finished reading the article :P He talks about death briefly at the end. I still strongly disagree, and would jump at the chance to live forever, although it's definitely scary to think about. I would always want to have suicide as an option, for unexpected events such as a life in prison, or never-ending torture.
The human brain is definitely not equipped to think about timescales on the order of Graham's number, but I would probably only be "human" for an infinitesimally small period of time, relatively speaking.
One day someone from the future might stumble upon these comments and laugh. I hope we make it that far, as a species.
ETA: the article gives a sense of vastly hugely mind-meltingly large numbers; when considering a number so staggeringly gargantuan is just an infinitesimal speck at the mere beginning of "forever", the thought of living that long becomes crushingly daunting. I suggest potential downvoters read the link first.