The University of California Museum of Paleontology‘s DinoBuzz site presents the question: Are Birds Really Dinosaurs? I encourage you to read the entire piece, which goes into much more depth, but here I have excerpted some key points from the answer:
Ask your average paleontologist who is familiar with the phylogeny of vertebrates and they will probably tell you that yes, birds (avians) are dinosaurs. Using proper terminology, birds are avian dinosaurs; other dinosaurs are non-avian dinosaurs, and (strange as it may sound) birds are technically considered reptiles. Overly technical? Just semantics? Perhaps, but still good science. In fact, the evidence is overwhelmingly in favor of birds being the descendants of a maniraptoran dinosaur, probably something similar (but not identical) to a small dromaeosaur.
Today the important issue seems to be specifically which dinosaurs are the closest relatives of birds. The controversy over the dinosaurian status of birds had its heyday in the 1970’s, but the coverage of the issue today by the press might make you think it was still a problematic matter. For those that have actually seen the relevant specimens and considered all of the relevant data (which is a basic procedure for any scientist), it is becoming increasingly difficult to draw the line between “bird” and “non-avian dinosaur”.
The opponents of the theropod hypothesis refuse to propose an alternative hypothesis that is falsifiable. This is probably because there are no other suitable candidates for avian ancestors. “Thecodonts” are often promoted as such, but this is an obfuscatory, antiquated term for a hodgepodge of poorly understood and paraphyletic, undiagnosible reptiles. The problems cited by such opponents for theropods are often more serious for the “thecodont” pseudo-hypothesis. Finally, such opponents also refuse to use the methods and evidence normally accepted by comparative evolutionary biologists, such as phylogenetic systematics and parsimony. They rely more on an “intuitive approach,” which is not a method at all but just an untestable gestalt impression laden with assumptions about how evolution must work.
The facts are resoundingly in support of a maniraptoran origin for birds; certainly a theropodan origin at the very least. So when you see a hawk diving to snatch a dove, or an egret darting for fish, or an ostrich dashing across the African savanna, know that you are gaining some insight into what the extinct dinosaurs were like.