Is there currently any way to privately send ether? If not, are there any plans in the future to implement any privacy features?
The sending and receiving addresses and the amount are available for anyone to view. (EtherScan for reference). In the future, Ethereum does plan to implement privacy features - zero knowledge proofs to allow for private transactions. See here. Also, Ethereum's plans for plasma would also extend privacy to parent chains off the root chain.
There are zk-SNARK related precompiled contracts that have been included since Byzantium in October, but AFAIK there is no user-friendly GUI for sending ZK transactions e.g. with MyEtherWallet.