There recently has been some discussion on the biblioblogosphere about whether the traditional attributions to the canonical gospels were original or secondary (henceforth, for sake of brevity, "gospels" unqualified will refer to the canonical gospels). I.e. did the "autographs," a textual critical term used to refer to what initially issued from the author, contain these attributions (thus making them original), or were they added later (and thus making them secondary)? Here is my contribution, for what it is worth.
The first thing to do is clearly define the question. I don't know if "Are the traditional attributions original to their respective gospels?" is quite the best question. My suspicion is that a better question would be something like "When did the attributions become associated with their respective gospels?" The first step is to see if we can't find termini post and ante quem for when this occurred. The terminus post quem would appear to be the initial composition of the gospels (and is inclusive of that composition). We probably cannot get more precise than that, as my understanding is that there is no known textual example of any canonical gospel circulating absent the traditional attributions (again, I emphasize that such a judgment lies outside of my primary area of specialization, so if I am mistaken then I would ask those who know more about such matters to kindly offer correction). That means that the attributions could conceivably have become associated with their respective gospels sometime between the initial composition of the gospels and the first clear evidence for these attributions in the extant data, which will provide the terminus ante quem (time before which).
We seem to have what we might call a "hard" and a "soft" terminus ante quem for the association of the traditional attributions with the gospels. The hard terminus is provided by the references to the four gospels that date from the late 2nd-century, perhaps most notably in the work of Irenaeus. A soft terminus would pertain specifically to the Gospels of Mark and Matthew, and date to the early 2nd-century. I call this a "soft" terminus ante quem, because the references come from Papias, and it is debated whether he is referring to our Gospels of Mark and Matthew here. My own judgment is that he almost certainly is, and his writings do suggest at the very least that by the early 2nd-century Christians were interested in learning about the origins of their written gospel tradition and more specifically that the figures of Mark and Matthew were closely associated with the production of written Jesus tradition. Given the above, we should conclude that the traditional attributions were associated with their respective gospels sometime between their composition and the late 2nd-century, with the Papian data perhaps militating against efforts to date the association of Mark and Matthew with their respective gospels later than the early 2nd-century.
Here we need to attend to an intentional word-choice in the formulation of the initial question. I did not ask "When did the attributions become attached to their respective gospels?" but rather "When did the attributions become associated with their respective gospels?" It is entirely conceivable that the texts initially circulated without any sort of written attribution. But it wouldn't follow that the early Christians weren't passing on oral reports about the origins of the texts. It's hardly inconceivable that if I'm a first-century Christian and I'm handed a copy of a text purporting to describe Jesus's life at length that I would ask "Who wrote this?", to which the answer might be, for instance "Mark." The Papian evidence suggests that such questions were being asked, the better part of a century before the hard terminus ante quem provided by figures such as Irenaeus, and one suspects that it can't be entirely a coincidence that the two names that he provides happen to be among the four names associated with the canonical gospels. Negatively, if one thinks that the attributions became associated with the gospels some considerable time later then one has to give an account for how the relatively late attributions became standardized so fast, with very little evidence of disputes about the attribution, and I'm not sure how well the extant data will allow us to give such an account. As such, given the state of the data, there's no reason to think that such a chain of tradition couldn't have started as early as the initial circulation of the gospels, some reason to think that it did, and good reason to think that it started several decades before the late terminus ante quem. Overall, I am inclined to think that the attributions likely became associated with their respective gospels relatively early, perhaps even from their initial circulation.
Note that I'm not here asking whether any given gospel was written by the figure to whom it is attributed, although, as I am always quick to point out, I do not think that the data is such that we can rule out such a hypothesis in the case of any of the four gospels. Certainly, if one is inclined, as I am, to think that the attributions became associated with these gospels relatively early, and if one is equally inclined, as I am, to think that the gospels were probably written somewhat earlier than the consensus view holds, then the case for the traditional authorship is probably strengthened. But even the consensus dates of the gospels, which situates the gospels between c. 70 and 90 C.E., cannot rule out the possibility that any or all of the traditional authors were stay alive and active, and the "late-association" hypothesis cannot necessarily rule out the possibility that the association, although late, was nonetheless correct. Still, again, that's not my question here. My question is how we might best think about when they became associated with the gospels, and my inclination is towards a fairly early moment in their circulation.