If so, how would it work and how much better/worse would it be compared to using a full node, especially the privacy implications. Obviously as Monero usage increases, end users should be using wallets that are accessible anywhere and a full node hampers that. How will end user clients work in the future?
The lightwallet by jwinterm is probably most similar thing to an SPV wallet so far https://getmonero.org/getting-started/choose
shen-noether is working on a mobile wallet that will connect to a remote node https://hellomonero.com/tags/shen-noether
Using an SPV wallet can have privacy concerns because the node that you use to relay your transactions needs to be trusted not to log and correlate your IP address with your transaction activity. These concerns can be eliminated by connecting to your own full node. Tools such as Monerodo OS (http://nodebox.link/) should make this process easier.
A framework is in place to support SPV wallets and more wallets are now being developed by Exodus and others. More focus may return to this area after RingCT is complete.
While it is true that relaying transactions to a node other than your own compromises (some) privacy, there are ways to create a mobile wallet that will address this concern. Basically, the wallet would only store the parts of the blockchain that are relevant to the outputs you own, plus some more to mix with when you create new transactions. There will probably be some slight compromises when it comes to ease of use, but privacy will be retained.