Counter-arguments for the naysayers
Almost everywhere when the subject topic of Immortality is brought up plenty of sources would be against the idea. Well we could be different, maybe living forever and the inability to die is a great state of being. People often side with religion that it is bad, some would use the justification of seeing people die, others use loneliness as an excuse. Common folk making lists of why people should not wan to live forever I say screw them, and the idea of being forever is simply wonderful. Some of us wanted more time to enjoy what the world has to offer, some of us do not want to die yet, while others simply wish to spend eternity on something that they love to do. Maybe it is adventure, I mean when you literally have all the time in the world at your disposal there isn't much that cannot be accomplished. So why do you like the idea of being immortal?
Different Kinds of Immortality
The TV Tropes Wiki uses the following categories:
Type I: Perfect Immortality: The character is immune to all harm, doesn't age, doesn't need to eat.
Type II: Undying: Immune to aging and disease, but can still be killed.
Type III: Regenerative: The character doesn't age, and heals quickly from any wound that doesn't kill them, but may die to sudden severe trauma. In some cases (think vampire), it takes specific types of injury to do them in.
Type IV: Resurrective: The character can die - or so it seems. They'll either grow a new body or transfer their consciousness to one that's already waiting.
Type V: Undead: Typically overlaps with Type II or Type III, but ghosts overlap with Type I. May or may not be creepy.
Type VI: Age Without Youth: The character cannot die, but shows their age. Could be said that this is immortality without the Required Secondary Powers.
Type VII: External: Immortality granted by a deal with the devil, demonic possession, soul jar or other Applied Phlebotinum. As such may be vulnerable to things that wouldn't harm a normal person, such as antimagic or an exorcism.
Type VIII: Legacy: The character can die, but their reputation or bloodline lives on. Think Dread Pirate Roberts.
Type IX: Parasitic: Like Type IV, except you force your mind into the body of some unsuspecting victim, and generally do so before the old body wears out.
Type X: Vampiric: The character is immortal, as long as they feed off the life-force of others.
Type 0: Non Diegetic: The character can't die because the author wouldn't dream of killing them off.
Neat read(s) about the subject