Currently, a bird is Archaeopteryx or anything that is more like a modern bird than Archaeopteryx is.
More accurately, 'bird' is not a scientific term, but a common one, and doesn't have any clear scientific definition. From an eviolutionary point of view, recognising that change is gradual, it's not too important where the exact line is between protobird and bird.
In scientific nomenclature, the birds are 'Aves', and the most common definition of Aves is the one that Dr. Adequate says - the common ancestor of Archaeopteryx and modern birds and all its descendants. This isn't the only definition though, and to try and clarify issues like this and give us clear, unambiguous definitions of groups of organisms, a mighty project is under way called
the Phylocode. This will give a standard definition for each taxon so that, in theory at least, anyone working in biology would be able to check exactly what you do and don't mean by 'Aves' (when it will ever be ready is an open question).
Under some of the proposed definitions, Archaeopteryx wouldn't make it into Aves, but whether or not you wanted to carry on calling it an early bird is a matter of taste. Common terms for animals always hit problems when you go back towards distant ancestors, that's why some bioogists decided they needed this unambiguous series of definitions for scientific nomenclature.
Edited by caffeine, : No reason given.