All of reality can be explained and predicted in a simple mathematical formula.
Although karma is a comforting idea, it doesn’t exist and ‘proof’ that it does are simply statistical outliers.
Jesus existed but was a regular guy.
Robin hood existed and stole from the rich to give to himself.
I can kill you with my brain.*
**I mean, I suppose I **could *prove it, but it seems rude.
I belive that they have found a cure for cancer but they won’t release it because there’s too much money that will be lost.
Yes, I know, I’m a crackpot. Come up with all of the reasons ya want to refute this but I still believe it. 
How about all the money it would make? Not to mention all the kudos you would get. “Hey baby, come here often? Last year, I cured cancer.”
I believe the uppermost strata of society engineers and controls the lower stratas to suit their agendas. I also believe we have the resources and the ability to drastically reduce fundamental problems like poverty, and maybe even war and crime, but the upper strata prevents this from happening. Indeed, they encourage these problems.
Yeah, but once you’re cured, that’s it. No more money to be made from medications and treatment and hospital stays. See, a cure is a one-time deal, no matter how much it costs, but the other stuff can go on forever!
I believe that dark matter, dark energy, string theory, multiple universes, and all such unprovable and unfalsifiable theses will be rendered trivially silly in retrospect when someone comes up with a more sensible explanation for what’s really going on.
The “somewhere” would be Catch-22, Dunbar IIRC.
I believe that humans will cause their own extinction. And it has already begun.
I believe that Australia would be better off if I was in charge.
Oh, but that one’s provable! I looked into the big brown eyes of my yellow Lab, Daisy – yup, dogs go to heaven. They deserve it.
I believe that excessive electronic stimulation (television, computers, movies, toys that go “beep”) makes kids a little crazy. They get wound up, their attention span diminishes, and they act aggressively and whinily.
(That one’s certainly “provable”, but I lack the resources to do it.)
I believe that the colder it is on the Port side of Florida during November and December… that it indicates an active and full season (Summer and Fall) of Gulf of Mexico Hurricanes in the next year. I think it even relates to the intensity of following Hurricanes.
Well, of course I can’t prove it! If I could prove it, I wouldn’t believe it now, would I? 
I believe that routine is calming, and adds years to life. And I don’t care if I can’t prove it!
Things I believe but cannot prove:
There is no afterlife. This is all we get.
There is life in other parts of the universe.
There are multiple universes.
This I believe:
In any closed system, the amount of entropy will increase over time.
Prove it? I can’t. But show me a counter-example or GTFO!
I have a sneaking suspicion that if there really is an epidemic of cancer and autism, and it’s not just that they’re more common because there’s more people and better diagnoses, then it’s probably partly due to pollution.
I believe that I’d vote for you.
No, you don’t. You’re a figment of my imagination. But I can’t prove it.
I look into my 10 YO Lab/Rott Bitz’s eyes or our English Bulldog’s goofy little countenance and simply know this to be true. There’s no way that much love, joy and devotion doesn’t get a just and eternal reward.
I’ve said before, and will say again, dogs ask of us only what we can spare and give in return all that they have. It’s the best bargain humanity ever made.
I believe that God exists and that there is life after death. For animals, too.
Some part of me still believes in Santa Claus. The idea of someone so kind and generous and magical makes me happy.
I believe in psychic abilities, but the moment someone claims to talk to strange dead people and charges people for their services, I call BS. I’ve had several psychic experiences myself, but they were very personal, were not anything I could conjure up by will alone, and were difficult to explain. But they happened, so I don’t doubt that others have these experiences as well.
I believe that love truly does conquer all.