There's an atrociously-reported series of articles being published that centre around one incredible claim: watermelons have viagra-like properties.
Except they don't.
Viagra works by inhibiting an enzyme that degrades cyclic guanosine monophosphate (cGMP). This cGMP keeps the vessels in the penis dilated (it relaxes smooth muscle), and so by preventing it from being metabolised, Viagra keeps the penis erect longer.
Watermelon's don't do this. They simply contain a substance that participates in forming nitrous oxide (NO). In the penis, NO causes an increase in cGMP - and this is where probably where the confusion lies.
However, this watermelon effect is totally non-specific to the penis. If it causes an increase in NO, then all smooth muscle will be affected. Also, since the breakdown of the cGMP in the penis will not be affected, this will not lead to a prolonged erection anyway.
Hmff. If you wish to know about the above in more detail - and replete with puns - look here. (I stole the title from one of the comments.)