Business Applications: What are the fundamental features of a search form?

Maybe it's a bit trite but there is some sense in this picture:

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Do it as it shown at the second example, not as at the 3rd one.

There is a well known extreme programming principle - YAGNI. I think it's absolutely appliabe to almost any problem. You always can add something new if it's necessary, but it's much more difficult to remove something what is already exist because someone already uses it even if it's wrong.

How about the ability to save search criteria, in order to easily re-run a search later. Or, the ability to easily, cleanly, print the list of results.

If search refining is allowed (given a search result, limited future searches to the current results), you may also want to add a breadcrumb system, so that the user can see the sequence of refinements that lead you to the current result-set -- and by clicking on a breadcrumb, return to a previous refinement stage.