I have personally been thinking about the nature of existence a lot lately, although with a different perspective (I was looking at it with regards to the existence of God). Also, for my sins, I'm currently studying philosophy at A-Level, hoping to continue at Uni, and one of the topics covered was philosophy of mind, which hints at the nature of existence.
Anyhow, getting to my point. Before we can decide whether we exist, we need to define existence. And therein lies the tricky part. A good example (and yes, I'm sorry, I'm going to have to refer to theology here) is the Ontological argument for the existence of God (I'm agnostic, btw). Anselm's argument is, basically, that God is that than which nothing greater can be conceived, that which exists in reality is greater than that which exists in the mind, therefore God exists. This raises 2 interesting points...it's not only existence that needs to be defined, but "reality", for surely, ideas "exist", even if they're just in the mind? Am I making sense? So existence is a nasty concept to try and pin down. An idea can "exist" in the mind, but not in reality, assuming that reality can be defined as the physical world. But then if you get into Quantum Physics, it gets tricky...Charms, Leptons etc (as far as I know) have only been proived to exist indirectly, so do they exist in "reality"? Now, where am I going with this...
Well, basically you can use Descarte's argument, it works...but if you can argue that something "exists" in the mind, then a heck of a lot of things "exist". So it's not a matter of
whether something exists, but rather
where it exists (e.g. in "reality" or the "mind").
Hope at least some of that is relevent/interesting
Amber