This issue is clouded by the fact that the meaning of the word ``dinosaur'' has changed over time - which may or may not be a good thing.
When the first dinosaurs were discovered, it never crossed anyone's mind for a moment that they might be ancestral to birds, so the original definition of ``dinosaur'' certainly didn't include them. Even with the discovery of Archaeopteryx in 1861, the dinosaur origin of birds was far from being accepted as fact. It's only really since Ostrom demonstrated the similarities between Archaeopteryx and Deinonychus in the late 60s that the theory has gained any respectability - and so, the idea that the dinosaurs even might include birds dates back only a few decades.
Since then, a fundamental shift in nomenclature practices has meant that this bird-inclusive definition of the Dinosauria is now accepted as orthodox. This shift has been towards a viewpoint often called the ``cladistic'' view (related to, but separate from, the issue of cladistic analysis), which is that the only groupings which may validly by given names are monophyletic ones - that is, those consisting of a single animal together with all of its ancestors.
This spells trouble for the old definition of the Dinosauria, which is essentially the common ancestor of the Saurischia and Ornithischia with all of its descendants except the birds. Such a grouping is described as paraphyletic and is considered by cladists to be an unnatural group. So as cladistic nomenclature has taken hold, so the newer, monophyletic and more inclusive definition of the Dinosauria has become accepted.
Is this change a good thing? Yes, because it means that Dinosauria are now defined in a way that's in keeping with widespread taxonomic practice. And no, because the change itself is disruptive, leaving what was once a clear meaning unclear. A similar situation has arisen with regard to the class Reptilia, which is considered to include the dinosaurs and hence also the birds. (So, yes, birds are reptiles!)
Some people, notably Ken Kinman, argue that it would have been better to make up completely new names for the inclusive monophyletic groups rather than re-assigning the old names. In his paper Origin of Birds: The Final Solution? (American Zoologist: Vol. 40, No. 4, pp. 504-512), Peter Dodson is particularly forthright:
For example, the word dinosaur was not previously problematic - it was universally understood. Within cladistics it has now been redefined to include birds [...] and then a new and cumbersome phrase, non-avian dinosaur, has been substituted. This is not progress; this is semantic obfuscation not enlightened communication.
In the alternative approach, the monophyletic group consisting of all dinosaurs including birds could have been given a new name - Eudinosauria, say - and reptiles including dinosaurs and birds given a new name such as Eureptilia. Whether or not this would have been a good idea, it seems that the moment has passed: it's not going to happen.
With all that said, I'm still going to continue hedging, because there is a big difference between technical nomenclature and everyday language. When we talk to non-scientists, they will understand the term ``dinosaur'' to include the likes of T. rex and Triceratops but not swans and sparrows. OK then, there's no need to rock that boat - let's use the word in accordance with people's expectations - in everyday life, ``dinosaurs'' generally means ``non-avian dinosaurs'' - or what I like to think of as ``Real Dinosaurs'' :-)
More than that, most of the time scientists also use the word ``dinosaur'' in the informal sense that excludes birds. For example, the Dinosaur Mailing List's administrative message describes the list's purpose as ``to give people a forum for the scientific discussion of dinosaurs.'' Yet everyone implicitly understands that this means non-avian dinosaurs: the list only ever discusses birds in as much as they are relevant to Real Dinosaurs.
So even scientists don't need scientific nomenclature all the time. Generally, though, the feeling is that it is better to stick with formal nomenclature for most technical discussion; and certainly in formal publications, in which misunderstanding would be disastrous.
As a rough rule of thumb, when people use latinate terms like Dinosauria and Reptilia, they often intend them to be understood in the monophyletic, inclusive sense; whereas informal terms such as ``dinosaurs'' and ``reptiles'' tend to carry their historical meanings. But this is by no means hard and fast.
In many technical contexts, the informal notion of Real Dinosaurs simply isn't rigorous enough for many uses. When an author wants to refer to dinosaurs other than birds, exactly which animals does she with to exclude? All of the Aves? Just the extant groups? The whole of the Avialae, or even all the Maniraptora? Or just the Pygostylia? In many contexts, it's necessary use an unambiguously precise term such as ``non-avialan Dinosauria''.
But we shouldn't allow that to blind us to the obvious - so that when we read that Spielberg is making a film about dinosaurs, we can be pretty sure it's not going to Sparrow Park.