Common name search
I would love to see a way to search a family tree with extended members (where I am working) that would show up the people with the same surname or even first name. The search could help me to follow a hunch, like several same first names of cousins that could likely be a relative they are named after that hasn't yet been found with manual searching, especially if it is an unusual name that shows up in several children. The surnames can help find some relatives that I don't have enough information about to get very far with a basic search. But if I have a hunch there are others with the same name on the tree and this might be a clue, perhaps a search that allows a listing of those related to me with the same names could help.
It's also interesting as a trivia item. Example: How many in my tree have the name of William?