Under what conditions does a multi-pass approach become strictly necessary?

I'd like to enumerate those general, fundamental circumstances under which multi-pass rendering becomes an unavoidable necessity, as opposed to keeping everything within the same shader program. Here's what I've come up with so far.

• When a result requires non-local fragment information (i.e. context) around the current fragment, e.g. for box filters, then a previous pass must have supplied this;
• When a result needs hardware interpolation done by a prior pass;
• When a result acts as pre-cache of some set of calculations that enables substantially better performance than simply (re-)working through the entire set of calculations in those passes that use them, e.g. transforming each fragment of the depth buffer in a particular and costly way, which multiple later-pass shaders can then share, rather than each repeating those calculations. So, calculate once, use more than once.

I note from my own (naive) deductions above that vertex and geometry shaders don't really seem to come into the picture of deferred rendering, and so are probably usually done in first pass; to me this seems sensible, but either affirmation or negation of this, with detail, would be of interest.

P.S. I am going to leave this question open to gather good answers, so don't expect quick wins!

Deferred / multi-pass approaches are used when the results of the depth buffer are needed (produced by rendering basic geometry) in order to produce complex pixel / fragment shading effects based on depth, such as:

• Edge / silhouette detection
• Lighting

And also application logic:

• GPU picking, which requires the depth buffer for ray calculation, and uniquely-coloured / ID'ed geometries in another buffer for identification of "who" was hit.