One step-down regulator 24 V to 1V or two step-down regulators with lower steps?
As the step-down (or step-up, for a boost converter) ratio gets higher, the duty cycle of the switcher gets less.  This means more switching losses, higher current than necessary in the switch, and general Bad Things all around.

The rule of thumb that was passed to me is that you don't want to exceed a 10:1 ratio before you either use a flyback converter or two stages of conversion.

A flyback requires a custom transformer, so you probably don't want that unless either your power levels are high enough or your manufacturing quantities are large enough to warrant that transformer.  Even with a flyback, unless you're converting a lot of power you may just want to drop to 3.3V and derive the other voltages from that using ordinary buck converters.

For small volume production and small power running two stages of buck converter is probably best; you'll want to do some design studies to see if 5V is the best intermediate rail, though.  (For that matter, you may want to do some design studies to verify that you don't want a flyback).