Middle English durren, daren, from first and third person singular of Old English durran "be bold enough, have courage" (to do something), also transitive "to venture, presume," from Proto-Germanic *ders- (source also of Old Norse dearr, Old High German giturran, Gothic gadaursan), according to Watkins from PIE root *dhers- "bold" (source also of Sanskrit dadharsha "to be bold;" Old Persian darš- "to dare;" Greek thrasys "bold," tharsos "confidence, courage, audacity;" Old Church Slavonic druzate "to be bold, dare;" Lithuanian drįsti "to dare," drąsus "courageous").
An Old English irregular preterite-present verb: darr, dearst, dear were first, second and third person singular present indicative; mostly regularized 16c., though past tense dorste survived as durst, but is now dying, persisting mainly in northern English dialect.
Transitive sense of "attempt boldly to do" is from 1630s. Meaning "to challenge or defy (someone), provoke to action," especially by asserting or implying that one lacks the courage to accept the challenge, is by 1570s. Weakened sense in I dare say (late 14c.) "I suppose, I presume, I think likely," now usually implying more or less indifference. How dare you? is from c. 1200 (Hu durre ȝe).