Wagner is notorious first and foremost for his vicious anti-semitism, which is all the worse considering how many Jewish musicians supported his career. In 1850, he wrote his infamous article "Das Judenthum in der Musik," in which he attacked the beloved German-Jewish composer Felix Mendelssohn and the popular grand opera composer Giacomo Meyerbeer. The timing of the article was especially cowardly, since Wagner apparently hid his noxious views until after Mendelssohn's death. The notorious article may have been motivated as much by jealousy as racism. Wagner deeply resents Meyerbeer for his popularity, despite the fact that the older composer had helped Wagner at a pivotal point in his career by ensuring a performance of Rienzi. In fact, earlier in his life, Wagner had greatly admired Meyerbeer, but his bitterness and racism alienated him from his one-time friend and mentor.
While his racist attacks on "Jewish music" were particularly loathsome, Wagner also proved to be a terrible human being in many other respects as well. Throughout his deeply troubled marriage to actress Wilhemine Planer, Wagner had multiple affairs (to be fair, she also left him at one point for another man, but they later reconciled). Famous for his love of luxury despite his poverty-stricken circumstances, Wagner and his wife also repeatedly fled from their creditors to avoid paying debts.
He treated his friends and patrons appallingly--in fact, he often seduced his close friends' wives. First, he had an affair with Mathilde Wesendonck, even though her husband gave him several loans and allowed him live to live in a cottage on their estate. Most famously, he carried on an affair with Cosima Liszt, the wife of Hans von Bülow, a prominent conductor who had dedicated himself to promoting Wagner's music (at least until he found out about the affair). Bülow had been a close friend of Wagner's, and he refused to grant his wife a divorce until after she and Wagner had three illegitimate children. He also defected to Johannes Brahms. Wagner's next favorite conductor, Hermann Levi, was hand-picked by Wagner to conduct the first performance of Parsifal at Bayreuth. But as a Jew who refused to convert to Christianity (despite pressure from Wagner), Levi suffered racial taunts and humiliations from Wagner's acolytes, and at one point Wagner considered firing him on account of his religion.
Of course, none of this makes the impact or artistry of Wagner's music any less powerful. As much as we might wish all great artists would be great people too, that isn't always the case. Wagner is a good example of how even terrible people sometimes have talent and artistic vision.