A lot of people say that they would like to live forever, me included. However, what would this do to a person? In Shadowrun, where some of the characters do live forever (the Harlequin being one), some spend whole centuries as raving lunatics.
What would this do to your humanity? If you knew that everyone around you was going to die and leave you alone how would you cope? Would you remove yourself from real relationships? How would you deal with them getting older whilst you stayed the same? How would they cope? What if you could have children?
Moving on, how would your thought process work? Would you take the long view when it came to plans? Would you start to put things onto motion, tweaking your plans over years, decades, even centuries? Would you use your ability to do good, or use it to destroy?
What would you do for pleasure once you had explored everything you wanted to? Would food cease to give you pleasure, would what is supposed to be a sociable and pleasurable activity become just a way of fuelling yourself? Would everything become boring, to the extent that you might actually want to die?
There are far more things to consider, but as you can see this is a rich environment for an author to explore. Have fun.