Imagine this: By some mysterious cause X you gain immortality. Time passes by and you have done all sorts of things on Earth, tried everything - maybe even managed to bed every girl you dreamt of. By this time, humanity probably will have developed proper interstellar propulsion systems and hence you venture out into the unknowing darkness. As millions and millions of years pass by you get to see all the wonders of the universe, you visit the Horsehead nebula, drink Johnny Walker with aliens from Betelgeuse, Jump through a wormhole butt-naked...
And now it's 5 trillions years later. You did everything there is to do, you went everywhere you can go. Met every celebrity there is and celebrities that were thanks to a timemachine/holodeck.
Now what?
For existence potentially being of infinite nature as well, I have no doubt in my mind that you would get bored quickly or even ever. 5 trillion year is a lot for someone that's not immortal, but for someone living basically for eternity it's quite literally nothing.
I think the idea that life is more worth when it's not infinite might very well be untrue as well, for it's actually the more memorable memories that count when it comes to the emotional experience of life itself. Not the fact that you may one day not live anymore. :-p
I do think the idea of immortality sounds great, especially as a severally increased lifespan (ie. literally infinite) really provides one with the ability to do a whole lot of otherwise impossible things.
You're still bound to change and progress or degradation of cultures, planets, life and so forth though, so it's not like you'll end up living an unrestricted life.
What if a culture decides to capture you as their 'God', holding you captive for thousands of years? Immortality obviously isn't the same as having unlimited physical, mental or 'magical' powers.
The immortality factor might not always be positive, but the same holds true for mortal life.
