alt Hacker NewsThe Interborough Express is one example. Going from southern Brooklyn on the water up to queens. Previous proposals had it also connecting to the Bronx. If you want to be really ambitious, connect Bayridge to Staten Island and continue on with branches to Elizabeth and Bayonne. Up north, it's surprising there isn't rail from the Bronx, through Manhattan, across the GW Bridge to NJ.
That's not what I'd understand as a "ring" though. I guess something like that could be useful in providing an alternative to what's mostly been car options for travel between Brooklyn and Queens. Edit - your more ambitious idea could be a "ring", yes, but I'm not seeing how it would be especially useful. Why would it be helpful to provide a single line allowing someone in Bayonne to get to Jackson Heights, for example (given what are probably more pressing transportation improvement needs)? As a visionary means of facilitating a longer term integration of eastern New Jersey communities to New York City, maybe.