In the Wars of the Roses, the descendants of King Edward III disputed the proper order of succession to the throne. Edward the Black Prince, who was the firstborn son of Edward III, predeceased his father, and the Black Prince's son, Richard II, was a terrible ruler. This led Lancaster and York to dispute the succession because the House of Lancaster traced its roots back to John of Gaunt, the third son of Edward III, while York traced its roots back to Edmund of Langley, fourth son of Edward III BUT also to Lionel of Antwerp, the second son of Edward III, though this was through Lionel's daughter. It was argued by Lancaster that the connection to Lionel was invalid, and York argued that it was valid. Lancaster won, giving England Henry IV, Henry V and then Henry VI.

However, Henry VI was so disastrous as king that the York faction was able to ultimately depose him (though he traded places with Edward IV as king, such that both kings had split reigns). After Edward IV triumphed over Lancaster, the York victory became worthless because Edward's children were murdered (though his older son was already considered King Edward V for numbering purposes), probably by Edward IV's brother, who became King Richard III. Richard, of course, was so unpopular that he was then defeated by Henry Tudor (Henry VII), who married Elizabeth of York to solidify what would otherwise be a shaky (very shaky, actually) claim to the throne. Elizabeth of York is interesting because she was the daughter, sister, niece, wife, mother and grandmother (in that order) of all the rulers of England from Edward IV to Elizabeth I.

To put that into the Game of Thrones template doesn't work because the time frame has been telescoped significantly, Stark and Lannister aren't branches of the Targaryen order of succession (and House Baratheon has no historical parallel at all). There is a very, very tenuous connection that says Robert is Henry IV (since Henry IV deposed Edward II), Joffrey is the short-reigning Henry V and Tommen is Henry VI. However, to follow this further then a Stark has to unseat Tommen, have children and then see his brother murder them, only to have Jon Snow challenge and unseat him and then marry the niece of the murderer-Stark.

However, I do think that Jon Snow is the most likely candidate to take the role of Henry Tudor and end the war. Regardless, there weren't wights riding huge spiders and killing all humans in the Wars of the Roses, so the whole thing really derails.