Obituaries of dead conjectures
$\mathsf{NL} \neq \mathsf{coNL}$. Prior to the result that these two were equal, I think it was widely believed that they were distinct, by analogy with the belief that $\mathsf{NP} \neq \mathsf{coNP}$ (i.e. the general principle that "nondeterministism and co-nondeterminism are different"; this turned out to be false under space complexity bounds that were at least logarithmic).