Sir Gawain, from Sir Gawain and the Green Knight, functions as an Arthurian hero. Similar to the heroes of the preceding generations, the hero needed to be loyal, generous, courageous, and uphold the Knight's Code. If looking at Sir Gawain from this perspective, he is most certainly a hero.
Gawain illustrated his loyalty and courage by accepting the challenge of the Green Knight. Not wanting his uncle (King Arthur) to take the challenge, Gawain rose to the occasion. His travels to find the Green Knight, a year after his oath, illustrates his honesty and courageous nature (he knows he may not survive a blow to the neck like the supernatural Green Knight--yet he still goes).
Sir Gawain also upholds the Knight's Code. He is loyal to God and Mary (seen with his prayer and shield). He also respects women (as seen with his numerous tests by Lady Bertilak (Morgan Le Fay). He keeps his promises to the Green Knight when he turns over the kisses he receives during the day.
Although he fails to give the magical garter/sash to the Green Knight, he did refuse the greatest of all challenges (sleeping with Bertilak's wife). Also, Gawain admits to keeping the garter/sash. Given that the Green Knight and le Fay were testing him, the Green Knight absolves him of any wrong doing. Gawain returns to Arthur's a true hero.