The Dungeons & Dragons concept of the adventurer as a professional individual that goes on adventures sort of has its historical antecedents, insofar as you could retroactively claim that there are individuals in the past that set out to seek their fortunes, whether as wandering knights, men-at-arms, traveling merchants, explorers, etc. - these are the kind of people whose activities could be chronicles as adventures and so they are adventurers by modern parlance. The particular concept of the D&D adventurer, however, owes more to literary developments of the early 20th century, for example Fritz Leiber's Two Sought Adventure (1957), a seminal collection of his stories of Fafhrd and the Gray Mouser. These two individuals were rather rootless and jack-of-many-trade types - thieves, swordsmen, sailors, etc. who got into many adventures. You might also compare Robert E. Howard's Conan the Barbarian, who was famously announced in "The Phoenix in the Sword" as:

Hither came Conan, the Cimmerian, black-haired, sullen-eyed, sword in hand, a thief, a reaver, a slayer, with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandaled feet.

Conan too was an "adventurer" in the sense that he was an individual of varied skills who went on adventures (which was a very broad category of events), and his stories are chronicles as such. In Dungeons & Dragons, the conceit of play was that a "party" of individuals were engaged on an adventure together (compare with the "unexpected party" in J. R. R. Tolkien's The Hobbit); this series of adventures could be strung out into a narrative campaign with the same characters. This eventually morphed into the concept of professional adventurers - that is, players created characters whose primary occupation and interest was "going on adventures" rather than being, say, a wandering man-at-arms. It's an unusual concept and the historical precedents are slight - probably mercenaries are the closest equivalent, although like I said, there were wandering professionals, merchants, knights, etc. during the medieval period that kind-of fit into similar roles - although usually not quite to the extant that D&D developed in fictional settings like the Forgotten Realms (introduced to players through Dragon Magazine in 1979).

The idea of "meet a guy in a tavern to get a job clearing out the local bandits" or the like wasn't typical of the medieval period; although you did get wandering knights who made a living off of hospitality and winning tourneys; mercenaries likewise tended to go where the action was, traveling to wherever wars were offing; in a less violent approach the same basic impulse caused troubadours to move from court to court, tinkers to go from town to town, etc.

I would like to add that we find motives in certain Icelandic sagas that are not too far away from the idea of some rpg adventures, specifically situations were the protagonists have to fight undead mound-dwellers (draugar, or haugbúar). At least on one occasion the fight is in the mound (hill-grave) itself and treasure and/or weapons are recovered. Grettis saga is the prominent example I would say. If there is interest here, I can add specifics next week, am on mobile in holidays. I don't think that there is any direct tradition or continuity that leads us to D&D, though.

Edit: oh, and that whole undead-slaying thing is not really Grettis or any other saga heroes 'profession' per se; he's an outlaw, sorta happens into it, and doesn't get much out of it except psychological damage. Also, I'm obviously talking about literature here (~1300).