The type of sign the OP references is called an interchange sequence sign. I think the one that Hobsini posted (in Madison, Wisconsin) is the only one so far cited in this thread that beats BigMikeLakers' Needles example. Other signs cited or described have longer distances but are not interchange sequence signs. In MUTCD terminology, the NYSTA sign saying "17 MILES AHEAD" is a variation on a NEXT EXIT plaque ("next exit" is implied in this case).
The main difference between an interchange sequence sign and a route confirmation sign, which has an identical tabular format, is that interchange sequence signs give the distances to the next few exits in sequence, while route confirmation signs give distances to places that do not necessarily correspond to specific exits, let alone ones listed in sequence.