I still have an outline of ROH depths my (very long time ago) sharper wrote. According to him:
Figures: usually 7/8 (14/16) and above, with most at 1" (16/16)
Dance: 1/2 (8/16) to 5/8 (10/16), with most in between at 9/16 **
Freestyle: 1/2 (8/16) to 5/16, with most below axel at 1/2, and most doubles+ at 3/8 (6/16)
Hockey: 1/2 (8/16) to 5/8 (10/16), with most at 1/2 (including NHL level)
Recreational: 1/2 (8/16) for indoor skating or 7/16 for outdoor skating
Shallower (big number) for more glide, deeper (low number) for more grip. Freestyle skaters tend to go deeper as they improve (need more control of edge on harder jumps), dancers tend to go shallower (more glide in and out of turns). He was a firm believer in staying as shallow as possible while still having the control you need for whatever you're doing.
** Dance has changed a lot since he wrote this, so this may not be an accurate reflection of what his clients would be using today, if he were still sharpening skates...