When I first read your question, I was sure it was a trick—after all, almost nothing I believe in I can prove. I believe the earth is round, but I cannot prove it, nor can I prove that the earth revolves around the sun or that the naked fig tree in the garden will have leaves in a few months. I can't prove quarks exist or that there was a Big Bang—all of these and millions of other beliefs are based on faith in a community of knowledge whose proofs I am willing to accept, hoping they will accept on faith the few measly claims to proof I might advance.
But then I realized—after reading some of the early postings—that every one else has assumed implicitly that the "you" in: "even if you cannot prove it" referred not to the individual respondent, but to the community of knowledge—it actually stood for "one" rather than for "you". That everyone seems to have understood this seems to me a remarkable achievement, a merging of the self with the collective that only great religions and profound ideologies occasionally achieve.
So what do I believe that no one else can prove? Not much, although I do believe in evolution, including cultural evolution, which means that I tend to trust ancient beliefs about good and bad, the sacred and the profane, the meaningful and the worthless—not because they are amenable to proof, but because they have been selected over time and in different situations, and therefore might be worthy of belief.
As to the future, I will follow the cautious weather forecaster who announces: "Tomorrow will be a beautiful day, unless it rains." In other words, I can see all sorts of potentially wonderful developments in human consciousness, global solidarity, knowledge and ethics; however, there are about as many trends operating towards opposite outcomes: a coarsening of taste, reduction to least common denominator, polarization of property, power, and faith. I hope we will have the time and opportunity to understand which policies lead to which outcomes, and then that we will have the motivation and the courage to implement the more desirable alternatives.