Foreman's maximality principle (the statement: any non-trivial forcing either adds a new real or collapses some cardinals) implies there are no inaccessible cardinal.
Also the consistency of Magidor's question (tree property at all regular cardinals above $\aleph_1$) implies the non-existence of inaccessible cardinals.
Another example is the following maximality principle introduced at A new maximality principle and its consequences:
$(MP_*):$ For all uncountable regular cardinals $\kappa, 2^{<\kappa}=\kappa^{+}$ and all trees of height and size $\kappa$ are specialized.