"One-to-many" routing, especially internationally; for instance, show all fares from a given North American airport to any Western European gateway. (Some sites sort of do this, but I have yet to find one that does it fully and easily.)

"Open jaws" fare quotes. Put in for instance an itinerary like outbound ORD-LHR return PAR-ORD and get fares for it, that is, quotes for round trip fares that allow open jaws without costing much more. Many airline sites do this, but not most comprehensive sites, and some that do just seem to give you two one way fares.

Showing for any multi-segment itinerary in any fare class if stopovers are allowed and if so how much it costs extra.

Quote special two-for-one companion fares offered on any itinerary in any fare class.

For any quoted fare allow an easy way of answering the question, "Is this exact same ticket also sold by another code-sharing airline and if so what is the cost?"