The 3 Sorting Hat Songs

There are three sorting hat songs in the Harry Potter books. These serve as our primary resource for determining the character of each house. Here is what each song tells us about these houses:

Book I

"You might belong in Gryffindor, Where dwell the brave at heart, Their daring, nerve and chivalry Set Gryffindors apart;
You might belong in Hufflepuff, Where they are just and loyal, Those patient Hufflepuffs are true And unafraid of toil;
Or yet in wise old Ravenclaw, If you've a ready mind, Where those of wit and learning, Will always find their kind;
Or perhaps in Slytherin You'll make your real friends, Those cunning folk use any means To achieve their ends."

Book IV

Describing the founders:

"Bold Gryffindor, from wild moor,
Fair Ravenclaw, from glen,
Sweet Hufflepuff, from valley broad,
Shrewd Slytherin, from fen."

Describing the selection criteria:

"By Gryffindor, the bravest were Prized far beyond the rest;
For Ravenclaw, the cleverest Would always be the best;
For Hufflepuff, hard workers were Most worthy of admission;
And power-hungry Slytherin Loved those of great ambition."

Book V

Laying out their manifesti:

Said Slytherin, "We'll teach just those Whose ancestry is purest."
Said Ravenclaw, "We'll teach those whose Intelligence is surest."
Said Gryffindor, "We'll teach all those With brave deeds to their name."
Said Hufflepuff, "I'll teach the lot, And treat them just the same."

Describing the selection process:

"For instance, Slytherin Took only pure-blood wizards Of great cunning, just like him,
And only those of sharpest mind Were taught by Ravenclaw
While the bravest and the boldest Went to daring Gryffindor.
Good Hufflepuff, she took the rest, And taught them all she knew,"

Summary of the Songs

If we ignore references to lineage, complexion and being treated equally (not metrics of personality) and presume that the descriptions of the founders are also salient, here is what the songs tell us about the character of each house:

Gryffindor: "Brave". "Daring, nerve and chivalry". "Bravest". "Brave deeds". "Bravest and the boldest". "Daring".

Hufflepuff: "Just and loyal". "Patient". "True and unafraid of toil". "Sweet". "Hard workers". "Good".

Ravenclaw: "Wise". "A ready mind". "Wit and Learning". "Cleverest". "Intelligence". "Sharpest mind".

Slytherin: "Those cunning folk use any means to achieve their ends." "Shrewd". "Power hungry". "Great ambition". "Great cunning".