My first impulse would be to say yes, however there are plenty of terrible implications both for me, and the rest of the universe if I truly got my wish.
Terrible Implications Affecting Me
Life would begin to feel futile and pointless, as you'd repeatedly make friends, see them die, make new ones, see them die, etc, etc. Looking back through history, one can see many patterns in the human race, and if you lived a sufficiently long time, life would get fairly boring. Oh sure, there may be period of great excitement, but since we're talking about living forever, those periods would be negligible in the grand scheme of things.
The Earth will not last forever. It will inevitably be destroyed, rendered desolate, etc, in one of the inevitable disasters that regularly occur (be them Gamma-Ray bursts, Sun collapsing/going Supernova, Asteroids, etc). So that leaves out chilling with the rest of humanity. Even bigger than just the Earth being destroyed, it is fairly likely that the Universe will collapse, expand too much, tear itself apart, or any number of the theories hypothesizing it's demise. Assuming you literally cannot die, can you imaging any fate worse than floating in a void FOREVER. Since your powers only include living forever, you would have no hope of ever escaping. And in such a circumstance, forever literally means forever. Never ending. Even death (assuming death means termination of consciousness), sounds better. Which brings me to my third point:
With the power of living forever, you would not be able to die, even if you wanted too. Although this may not seem so bad, consider the fact that in any bad situation, humans always have a guaranteed escape: death. Been abducted by a serial killer intent on torturing you? At least it can't last forever. Removing death potentially puts you in situations in which you would literally have no escape (such as the previously mentioned void thing). No hope, no nothing. You are literally screwed.
Many people would fear, envy, or desire to manipulate me because of my ability to live forever. Imagine the combination of a big-time celebrity (i.e Brad Pitt), whose doubtlessly the target of many scams, cons, etc, and an all-powerful dictator. I would either be a target for people who believe I could bestow upon them my powers (or to use me to generate wealth), or I would be feared because of my inability to die. Possibly both.
Terrible Implications Affecting Everything
The power of living forever is an immense one. It would make you literally unstoppable. You would essentially be a god. I don't think anyone, myself included, should have limitless power. While I don't subscribe to the saying "Absolute power corrupts absolutely" (it provides no reason why it allegedly ALWAYS does

), I can safely say I believe there is no way for me, or anyone else to know without a doubt, how to wield such a power. And even if they did, should they wield it?
Unless I abstained from raising families (as in, reproducing), or only allowed myself to have a family a couple of times (which would pretty much be the same as saying "No families", to an immortal being), I could corrupt the Human race's gene-pool. Since I would obviously be invulnerable to damage from radiation and other DNA corrupting things, my DNA would remain exactly the same forever. As such, if I had sufficient children, my genes could become the dominant ones in the gene pool, which means making genetic diseases that I doubtlessly have recessively stored in my DNA, common. Perhaps I have a gene that causes Alzheimers, though in my case it's recessive and doesn't effect me. If I passed that gene on a sufficient number of times (we are talking in the thousands, but remember, such a number would be a paltry sum to an immortal being), it could become common in everyone's DNA, as my children reproduced, and their children, etc, etc. Not to mention the fact, that eventually, most of the population would in some way be my descendant, which is kind of nasty if I were to keep on having more and more families

.