All transactions, which impact all nodes, have an associated transaction fee as one level of protection against Denial of Service attacks. The size of these fees will depend on the specifics of the transaction and the corresponding burden it places on the network.
There are three queries (which impact only a single node) that are currently free:
1) Asking for a receipt for a transaction.
2) Asking a node how much a particular query would cost, if actually sent.
3) Asking for the balance of an account.