Pedersen commitments, what happens if I choose $H$ such that $H = a\times G$?
If the committer knows $a$, then it is no longer binding. 

For any $m$ you commit, the commitment will be $(m+a)G$, so it is easy to find $m'$ and $a'$ such that $m'+a'=m+a$ to open the commitment.

Edit to add:
If the receiver knows $a$, then it is still information theoratically hiding because the sender chooses $r$ which is uniformly random.