What's the non-critical paths?

Static signals are the most common. (You might have something coming in from the board that is tied off at the board level.) Another example I recently saw was a design with a "test mux" built into it, pulling out test points from various parts of the design. Though I would recommend SignalTap, the test muxes select lines will not change, so can be ignored.

I've seen status signals get flagged this way, as they may change very sporadically and do not need to be updated. If they're synchronied in the new domain(so they don't go metastable), then the user doesn't need to be updated immediately and doesn't need to meet any sort of timing.

Just some examples.