Probably a lot of things, but two of them come immediately to mind: (1) The non-existence of a divine being who created the Earth, and (2) the non-existence of any pieces of DNA that would, regardless of the cultural environment a person was born into, consistently predispose a person to be more attracted to the same or other gender(s) than other people are.
Actually, I consider the existence of anything that anyone I know ever seems to have in mind when they use the word "God" to be so absurd that it verges on the disproven, even though it doesn't technically quite get there. But the existence of the specified type of DNA is harder to disprove. In my more confident moments, I can often feel it's about 95% disproven, but I never feel it's 99.999999999 plus a googolplex more 9s on the end % disproven, as I feel about most people's bizarrely specific ideas of "God."
Okay, now I'll challenge myself to come up with other things I believe without being able to prove:
I believe that even people who have no apparent consciences are really not happier due to their feeling bothered by other people's pain than they would be if they did feel bothered by other people's pain.
I believe that even though the time and money I save by avoiding television and movies is definitely a relief to me, the time and money I spend on books is somehow not actually just a similar escapist bad habit that I should give up.
I believe that even though I do recognize that it's not particularly other people's fault if they never received a decent enough education to be able to spell or punctuate above a fourth-grade level (and I feel significantly more torn about not pursuing romantic relationships with those people than I feel about not pursuing romantic relationships with highly educated people who hold irrational religious beliefs), I could never really be happy enough in a romantic relationship with someone quite that unable to share in or comprehend my love of language for pursuing such a relationship to be worthwhile for me. (I don't require perfect spelling or punctuation, by any means. I just don't want to find errors in more than half the sentences someone writes, unless they have another language that they write much better in.)
I believe that the time I save by not exercising much and the unpleasant tongue-experiences I spare myself from by not eating vegetables ever will ultimately prove to be well worth any potential negative effects that either of these things might have on my health (despite frankepi's occasional efforts to convince me otherwise).
I also appear to believe, rather bizarrely, that making sure I answer this question as thoroughly as I possibly can is so important that it's worth reading through the titles of all the entries in your entire current journal, in a futile search for that entry I remember you posting in which you mentioned this question once before and tried, I believe, to provide your own answer to it. Because I don't want to accidentally miss something important you might have mentioned that I'd realize that I believe in too! But I did not succeed in finding your entry, so you're in luck - you get an actual uncorrupted original answer that I was forced to think of all by myself.
2. Do you believe in an inner sense of gender? That is, do you believe that you can feel male or female in a way that goes beyond the sum of your body's physical shape and your upbringing and cultural experiences?
No. I occasionally read things that cause me to vaguely consider the idea that there might be a very, very minuscule such sense, but I invariably conclude that even if there is, it's too minuscule and hard to prove one way or the other to worry about bothering to believe in at all. (So I guess this should go under #1 as well!)
3. If you could instantly eliminate one type of prejudice (e.g., religious, racial, gender-based, orientation-based...), what would you choose to eliminate and why?
This is a cruel question to subject me to! Um . . . I think the most horrific mass-scale destruction going on in the world today (and noteworthily - is that a word? - tomorrow too, by virtue of ongoing irradiation from the depleted uranium weapons) is the destruction of the Middle East by the U.S. So I guess the question becomes: What type of prejudice is driving that? And I think it's more about monetary prejudice than it is about race-based or religion-based prejudice, even though those are certainly involved too. But then, it's also about nationalistic prejudice, and I'm not sure whether it's more about nationalism or about classism. I mean, the U.S. doesn't typically invade rich countries, but it also doesn't typically drop literal bombs on the American underclass. But I think nationalism will be much easier to eliminate in a realistic manner (through people getting to know people from other countries, via the Internet) than classism. So classism is the type of prejudice I'd choose to eliminate via the magical instant prejudice-elimination machine.
4. What do you think is your worst flaw?
I think I get on slightly more people's nerves than I'd ideally prefer to, by phrasing my opinions more vocally and untimidly than most people would probably do even if they had exactly the same opinions. But I'd hate to have the opposite flaw and care unreasonably much about what other people think of me, so it's hard to adjust the pitch exactly right.
I would also like it to be more difficult to provoke me, in an argument an online flamewar, into responding to insults or other bad verbal behavior with similarly bad (or possibly even slightly worse) behavior of my own. But I don't actually think I'm any worse than the average person about this; it's just something I'd like to be drastically better than the average person about, and I'm not drastically better.
I think the reason I gave two answers to this question is that I'm not sure how to interpret the term "worst." My first answer addresses the flaw that I think most nearly approximates what the majority of other people would probably call my worst flaw, while still being something that I actually do consider to be a flaw. But my second answer addresses the flaw that I'm probably a bit more concerned about actually trying to fix (maybe because it bothers me more or maybe just because I think it's easier to fix - I'm not sure exactly how to separate the causes, because the fact that I think it's easier to fix might be the reason I'm more bothered by not having fixed it yet).
5. If you could give up all desire to ever be in a romantic relationship, would you want to?
Oh my, it's never occurred to me to imagine that such a thing would be possible. But . . . no, I don't think so, because part of the fun of life is that there has to be something difficult about it, and I don't think I'd have much difficulty left at all if you took that away. However, if you asked me whether I'd want to be able to give up all desire to ever get married, I'd have a more difficult time deciding. Having romantic relationships might still be difficult enough to be satisfying, without having the added pressure of wanting them to actually last for the rest of my or the other person's life or necessarily become cohabitational or even short-distance. I often envy people who don't want those particular things from their romantic relationships, because it seems so sensible of them in a lot of ways. But on the other hand, if I were totally convinced that it was better not to want anything marriage-like, I'm sure I'd acquire the ability to stop wanting it! So I guess that means I don't actually want to give up all desire for that either.