Designated Hero: Wagner had a classical sense of The Hero, i.e. someone who is the protagonist of his story and whose actions have consequence, and not necessarily someone that the audience is supposed to identify with on a moral level (which is the more contemporary notion of a hero):
There are some people out there who cannot stand Siegfried, whom they view as a bully and a boor. The anti-Semitic connotations with his treatment of Mime don't help. And he rapes Brunhilde under the disguise of Gunther, which is pretty despicable; even if he was under the effects of Love Potion, he still saw it as no big deal to kidnap a woman on behalf of someone else.
Wotan's pretty openly a Manipulative Bastard, the Rhinemaidens taunt Alberich cruelly for their own amusement, Alberich is as miserable as he is power-hungry, and Siegmund and Sieglinde are incestuous murderers. Brunnhilde is arguably the only sympathetic protagonist, being manipulated rather than knowingly choosing evil, and accepting her Heroic Sacrifice to try to undo the crimes of everyone else.
Designated Villain: By the same token, a number of antagonistic characters are dealt with rather harshly.
Fasolt, an honest, humble and lonely giant who is genuinely in love with Freia and believed the building of Valhalla to be a sort of Engagement Challenge. Unlike the vast majority of characters, he doesn't go crazy about the ring until Loge advises him to get it (and even then, it's not world domination that matters for him but the memory of Freia's look).
Arguably Hunding. While he is a gruff and unfriendly man with a bad relationship with his wife, he is honourable (keeping his promise to let Siegmund spend the night), and according to the customs of his own culture he has done nothing wrong (it is clearly indicated that forced marriage is normal in the story's culture). He may want to kill Siegmund, but Siegmund has killed members of his clan.
Ear Worm: The constant Heijahei phrase to signify joy. Especially when the Rhinedaughters belt out "RHEINGOLD RHEINGOLD... HEIJAHI" in the cycle's first act. It recurs in the famous Ride of the Valkyries too.
Ending Fatigue: It's worth noting that, in the era when the cycle was composed, patrons were expected to make an all-day event of them, bringing meals with them to the performance and even going home to freshen up during intermissions. Those unfamiliar with this fact therefore have a tendency to accuse the cycle as simply being "too long."
Epic Riff: "The RIDE o' th' VAAALK'-ries, RIDE o' th' VAAALK'-ries, RIDE o' th' VAAAAAAAALK'-ries, RIDE o' th' VAAALK'-ries."
Or: "Kill da wabbit, kill da wabbit, kill da waabit!"
Harsher in Hindsight: Wotan punishes Brunnhilde for disobedience by stripping her of her power and reducing her to the status of a lowly wife. In Wagner's time, this would have been the standard role for a woman and would possibly have been seen as an Ironic Hell; however, in today's more emancipated world, many women can easily empathize with Brunnhilde's horror at the prospect.
Memetic Mutation: The expression "It ain't over till the fat lady sings" is very possibly a reference to the end of the Ringnote although an even better case can be made for Tristan, which actually ends with Isolde's Liebestod. The last scene of Götterdämmerung, features Brunnhilde singing a exceedingly long farewell to the dead Siegfried („Starke Scheite schichtet mir dort!note "Stout timbers stack for me there!"), although the very last vocal utterance of the work is Hagen's „Zurück vom Ring!"note "[Keep] back from the Ring!".
Newer Than They Think: Wagner's depiction of the three Rhine-daughters is largely a creation of his own imagination; though wise-women appear in the Danube in the 12th century Nibelungenlied, there is no indication that they are native to it, much less the daughters of its personified god, and they never go near the Rhine at all.
Pacing Problems: It has been opined that some scenes, such as Wotan's recap of previous events to Brünnhilde (in Walküre), go on way too long.
Seinfeld Is Unfunny: Wagner's „Musik der Zukunft" ("The Music of the Future") was considered daringly, even outrageously, innovative in his own time, but he became so influential that his music is now reckoned old-fashioned and even stereotypical by some.
Sequel First: Das Rheingold was actually the last of the plays to get an American production.