The problem is that SuperNET apps are mostly designed to use Jay. And what Jay does is that it connects to random public nodes (to increase decentralization and the user would not have to install Nxt locally and download the blockchain. Even though, we still open the possibility and recommend the user to install Nxt). What Jay will do most of the time when a user runs SuperNET Lite for example is connecting to strong nodes in the network. And these strong and reliable nodes are expected to run the newest stable version. So once this newest stable version (like 1.6.2) breaks the existing API, all SuperNET apps will not function in this case.
This explains a lot and also means that you cannot compare this situation to other centralized APIs.
This is once again a situation where we are the first to deal with, from decentralized development and deployment to actual usage of the system.
The other issue is the rapid development of NRS features, it's hard to remain stable if you are adding new features and reworking the internal structure very often.
Only solution I can see right now to solve this for the good on both sides is API versioning.
Yeah, it's good to be making history, though I'd prefer to do it a bit more quietly.

The above point on SuperNET (via Jay) connecting to random public nodes is important: this allows a short term workaround by only using 1.5.15 nodes, of which there are still about 100 running. This could also help other projects who may have issues with 1.6.3.
Having a blockchain download available for 1.5.15 would be useful, btw.
For a long term solution, we need to raise our project management game, and by we I mean mostly Nxt.
James is right: people need to be able to completely trust that Nxt will provide a stable basis for their projects. If we lose that trust, Nxt will be just another crapcoin, because no-one will build on the Nxt platform.
However, we cannot maintain backwards compatibility indefinitely. Nxt needs to advance and evolve, otherwise we become a dead system.
What we now need to do is to create a project management structure that will maintain that trust, while allowing Nxt to evolve.
The first steps were taken last week, by appointing Riker to the project manager position, and starting with set-up of a communication channel for all Nxt/SuperNET related project devs and the core Nxt devs, so we were already getting a structure in place to avoid this. Slightly late, though.

Myself and Damelon are working out little asses off to get this sorted out with everyone concerned, so I'd like to ask the community to chill out for a few hours, and allow us to figure out a long term solution.
In the meantime: as an immediate solution (if needed) advise projects to roll back to 1.5.15, and maybe some node operators could do the same.