As a literary form, the gospels have a lot in common with biographies. They also have many similarities to martyrologies, lives of philosophers, and even the aretologies (stories of virtue) of heroic figures. Ultimately, though, the gospels seem to represent the introduction of a new type of literature.
The canonical gospels have always been grouped together in the New Testament, separated from the various letters and other texts. It seems, then, that even the earliest Christians had a sense that there was something about these writings that distinguished them from other types of literature.
The word gospel stems from the Middle English godspel (god: good, spel: news) which itself comes from Greek and means the good news of some important event (like a birth or a victory). The intermediate Latin evangelium is well-known and itself in widespread use for the same concept as that communicated by the original Greek euaggelion (eu: good, aggelion: news).
The term gospel appears often in Pauls letters in reference to the significance of the person, life, and ministry of Jesus. Justin Martyr was the first to refer to gospels in the plural, around 150 CE, and today the term is limited almost entirely to the four canonical gospels that appear in the New Testament: Matthew, Mark, Luke, and John.
All four canonical gospels are characterized by certain common elements: stories about Jesus life, collections of Jesus sayings and teachings, and accounts about Jesus conflict with authorities, passion, death, and resurrection. Everything is brought together in a single connected narrative structured not according to historical chronology, but rather according to theological and political agendas.
Today the consensus among scholars is that the gospels are their own, unique form of literature they are sui generis rather than simply the extension of some other form, such as the biography. One important factor in this is the way in which Luke and Matthew are so heavily dependent upon Mark, making the nature of the gospels largely dependent upon the nature of just Mark itself.
It has been argued that Mark is not simply a product of the early traditions, stories, and sayings about Jesus if that had been the case, then Mark would like much like the biographies of philosophers or religious figures. Instead, Mark is a combination of such stories with the charismatic preaching traditions of the early Christian church. This, then, created a unique matrix in which a new literary genre could develop and then quickly die off, as the nature of Christianity changed and the canon closed to new additions.
While this represents the current consensus among scholars (and there is much to be said in defense of it), it is by no means uniformly accepted. There is quite a lot of work going on to see if there are actually much stronger parallels between Mark and Hellenistic literature, both biographies and heroic epics. Dennis R. MacDonald, for example, argues that there are impressive parallels between the structure of Mark and that of Homeric epics.
There is also work being done to draw closer parallels between the gospels and traditional Jewish literature for example, the biographies of religious figures such as Moses. The fact is, though, that Mark was composed in the context of Hellenistic Judaism and as such it should be expected to draw from both traditions. If that is the case, then it may be unreasonable to assume that Mark is predominantly a form of literature belonging to one or the other. If nothing else, a strong argument for the gospels being their own literary form can be founded on this.
One note should be made about the noncanonical gospels: there are many ancient texts relating stories about Jesus life or teaching which were not accepted in the New Testament canon but which are labeled gospels. In some cases, though, the label is inappropriate because they lack an overarching narrative structure or the preaching of Jesus message. Just because a text collects stories or saying of Jesus doesnt make it a gospel.

