Ah, I love this subject... although I'd have to admit I haven't thought about it for a long time.
I used to have a lot of arguments with a friend* over the fact that I'd claim to be non-existent. The theory was that, at the time, I'd done nothing of note with my life. I'd had no profound effect on the world or anyone in it. If I were to have died right there and then, there would've been no living trace of my existence, so did I really exist at all? Possessions and memories would've been all that remained. Possessions get lost or fall apart, memories fade... nothing is permanent. Any record of my existence is just paper and data. Paper burns, data can be deleted, corrupted or edited beyond recognition.
I think it's still true, now I come to consider it again. Since then I've had a fairly long relationship followed by a less-than-brilliant breakup, but people get over broken hearts... so does that count as living proof? Something that happened years ago and may be remembered but isn't a functional issue in any way? I don't think it does, so I'd still argue that it's difficult to prove I exist in any meaningful way.
I suppose the idea is that we're all just insignificant little creatures spending a very brief moment on the face of a planet that won't remember us when we're gone so, unless we do something to make our mark, we might as well have never existed. It's all about definition, I suppose; whether you take "might as well have never existed" to mean the same as "never existed".
[small]* For the record, the reason this caused so many arguments with my friend is that she somehow took it to mean that I was depressed or suicidal. That's not the case, and never was. I'm actually quite content with my life, as meaningless and insignificant as it is (indeed, as everyone's is) on the universal level.[/small]