The stag is both James’ Animagus form and the Patronus that Harry conjures. Since J.K. Rowling has said there is a connection between Godric Gryffindor and Goodrich’s Hollow [1], and since the Medieval Latin etymology of “patronus” is “patron saint,” could the stag be a clue to a connection between the life of St. Godric and Godric Gryffindor, and by extension, a clue to a connection between Godric Gryffindor and Harry?
The Stag and the Fidelius Charm
St. Godric is “noted for his close familiarity with wild animals” and is represented in art as a “very old hermit dressed in white, kneeling on grass and holding a rosary, with a stag by him.” [2] In the legend of “St. Godric and the Hunted Stag,” a hunting party is pursuing a particularly beautiful stag, which runs to St. Godric’s hermitage for shelter. St. Godric lets the stag in, but the hunting party follows the stag’s tracks and cuts through “the well-nigh impenetrable brushwood of thorns and briars” to find St. Godric. They ask St. Godric where the stag is, “but he would not be the betrayer of his guest.” [3] This legend parallels the workings of the Fidelius Charm, with St. Godric as the stag’s Secret-Keeper. However, unlike Peter Pettigrew, St. Godric does not tell the hunters where to find their prey, and the stag survives.
The Protection of the Privet Hedge
The “well-nigh impenetrable brushwood of thorns and briars” in the legend of St. Godric and the Hunted Stag parallels the privet hedge, which protects Harry from Voldemort when he is with the Dursleys; a protection Voldemort refers to as “ancient magic.” [4] In an interview, J.K. Rowling said that Harry won’t know for a “little while” the “whole truth” about why he is protected as long as he lives with his family. [5] Perhaps the protection is “ancient” because it is derived, in whole or in part, from Godric Gryffindor.
Boggarts and Dementors
The stag is not the only parallel between the life of St. Godric and Harry. When St. Godric became a hermit, he “is said to have been troubled by fiends and demons who took various shapes and forms.” [6] Harry is particularly troubled by the Dementors, and his boggart takes the form of a Dementor. It is the Patronus of the stag that saves Harry from the Dementor’s Kiss—the very animal that was saved by St. Godric.
The Gifts of Prophecy and Prescience
St. Godric had the “gift of prophecy, and the ability to know of events occurring hundreds or thousands of miles away.” [7] These are abilities also possessed by Harry. Harry has had numerous dreams in which he demonstrates his ability to know of events occurring far away from him—when he dreams of Voldemort and Wormtail plotting his murder and witnesses Voldemort’s murder of Frank Bryce; [8] when he falls asleep in Professor Trelawney’s class and hears Voldemort and Wormtail discussing Barty Crouch Jr.’s murder of Crouch Sr. [9] Harry also has the gift of prophecy, for in a dream about Professor Quirrell’s turban (before he becomes aware that Voldemort is underneath it), he hears a high, cold laugh and sees a “burst of green light;” [10] during his Divination final in his third year, Harry accurately predicts that Buckbeak will not be executed, despite Professor Trelawney’s efforts to change his mind. [11]
Choosing Good over Evil
St. Godric was not always saintly. Before he became religious, “he was known to drink, fight, chase women and con customers. Even when he became religious, he had to struggle to control his impulses. He would stand in icy waters to control his lust.”[12] As Professor Dumbledore tells Harry: “It is our choices…that show what we truly are…”[13] Harry is faced with choosing good over evil in the face of temptation, and much like St. Godric, he chooses good (despite “a certain disregard for rules”[14]). Moreover, it is Godric Gryffindor’s ownhat and sword (and possibly his own phoenix Fawkes as well [15]) that assist Harry in his battle against the evil basilisk in the Chamber of Secrets.
A True Gryffindor
As Professor Dumbledore tells Harry when he sees Godric Gryffindor’s name emblazoned on the silver sword Harry used to kill the basilisk: “Only a true Gryffindor could have pulled that out of the hat.” Could these many connections between Harry and the life of St. Godric suggest that Harry is actually a descendant of Godric Gryffindor? If so, Harry would then be the truest Gryffindor of all.
[1] Fall 2000 BBC Newsround
[2] http://catholicsaints.info/saint-godric-of-finchale/
[3] 
http://celticsaints.org/2014/0521c.html
[4] GF33
[5] BN
[6] http://www.thenortheast.fsnet.co.uk/DurhamCityVillages.htm
[7] http://catholicsaints.info/saint-godric-of-finchale/
[8] GF2
[9] GF29
[10] PS7
[11] PA16
[12] http://catholicsaints.info/saint-godric-of-finchale/
[13] CS18
[14] CS18
[15] Regarding the theory that Fawkes was once Godric Gryffindor’s phoenix, see essay “Fawkes and Gryffindor.”