I'm immortal because I can be and or I have no good reason.

I personally really dislike the use of immortality due to it being such an easy thing to make over powered, and it practically defeats the concept of living. Too many times have I seen people give it to already powerful OCS, or to an OC with a story and character that clashes horribly with immortality. Than there's the common mistake of mixing up immortality, the inability to die, with invincibility, where nothing can hurt the character in any way shape or form. That being said, used correctly it can be amazing and a interesting power and I'm definitely not saying don't do it. I personally have one 'immortal' character who's immortality I've limited to be both a small part of them as well as an incredibly large part of them, this character RP21 who is unwillingly kept alive after facing events that would kill a mortal dead, ie being eaten by a Velzdra or drowning. 

Immortality should be regarded as an extremely rare power that the character should not be 'born with' or just 'have' unless they are Gods or Goddesses, even than the idea should be used carefully. Like any power of this level, the character should of had to gone through the gates of hell to get this ability or payed a very big price to get it, it should have a negative consequence or certain conditions that keep it balanced and not usable 'willy nilly'. Perhaps it was given to them for their destiny. To give it a twist don't always see this ability as a gift, perhaps it's a curse for the character that they seek to get rid of.

The main pointer is this is a power that, if used correctly can create a terrifying character, having this power should compliment their personality and story, and be entwined with their beliefs, morals and psychical capabilities.

It's to be kept in mind there should always be a way to 'strip' this power from a character. Used wrongly it just makes a character annoying, unreasonable (ie being a species that shouldn't have this power) and devoid them of one of the most powerful plot devices; vulnerability.