The moon one is quite popular and some people put the 'evidence' that we haven't been across quite convincingly. Mythbusters did a great show though talking through the 'evidence' that we haven't been and doing some experiments - there verdict was the Myth is 'BUSTED' (e.g. we have been to the moon).

I am not a fan of conspiracy theories either - will have to think if have a favorite, but I always think is either a conspiracy or a C O C K up then is 90% chance is a C O C K up - and I reckon most conspiracy theories require more secrecy and planning than we are capable of (especially in this day in age keeping secrets seems almost impossible)