I think that immortality would have a lot of disadvantages and would cause a great deal of social disruption that would be hard to deal with. For example, if the death rate plummeted to near zero, but people still kept having kids, the population would quickly expand, causing much greater strain on our supplies of natural resources and living space.
In addition, a lot of people have contended that immortality would lead to a decrease in creativity and innovation. In science fiction stories, for example, societies of immortals are often portrayed as being static and decadent, with no great progress being made either scientifically or culturally.
Of course, from a personal standpoint, I don't want to die, but I can't really see immortality as being a good thing for humanity given its current position. Perhaps in the future if we have expanded into space and have advanced to the point that we can make sensible use of our resources, then it would be more advantageous.
There was a somewhat interesting TV show back in the '70s called "The Immortal," but unfortunately it did not really deal with many of these issues, being more of a chase/thriller series. It was based on a novel by James Gunn of the same title.