I'm a PGY-1 at the Yale Psych program, so I can answer your question.
R1 Medicine (~6 months): 4 months of q4 o/n, 2 months no call (though breakdown depends on the medicine site: YNHH/VA or St. Raphael's Hospital)
R1 Psych (4 months) and R1 Neuro (2 months): no call first month (to help get practical experience before taking call), then about q7-q10 o/n
R2: also about q7-q10 o/n
R3: about q7 12-hr o/n psych ER shifts (with full post-call day off afterwards) for 1/2 of year, then no call other 6 months
R4: call-free 🙂
Call can be quite busy (and difficult), but as you can see, the volume of call shifts isn't too bad.