During Sunday night’s Emmy Awards telecast (5 p.m PT; 8 p.m. ET, CBS), TV bigwigs will pat each other on the back, toot their own horns and hand out a lot of shiny trophies.

Those gold statuettes are supposed to celebrate television’s best and brightest — the pinnacle of what the medium has to offer.

But c’mon, we all know that Emmy voters often get it wrong. Sometimes stupendously wrong.

In fact, history demonstrates that there are a surprising number of extraordinary — even landmark — shows that failed to capture a single Emmy. Not one.

“That’s crazy!” you say. But it’s true. Here, have a look:

“The Wire”

HBO’s epic drama about Baltimore-based cops, drug dealers, corrupt politicians and more is generally considered to be one of the greatest TV series of all time (Rolling Stone, for example, ranks it No. 2 behind “The Sopranos”). Hall of Fame material, no doubt.

Yet, it received only two measly nominations (2005 and 2008) for writing across five incredible seasons, with no wins.

Just chew this one over for a few minutes: “Picket Fences” has way more Emmys (14) than “The Wire” (0).

“Star Trek”

The innovative sci-fi series boldly went where no show had gone before and its vast influence has stretched well beyond its three-year run on NBC in the form of countless spinoffs and imitators.

Still, Kirk, Spock and company failed to capture any of the 13 Emmys for which they were nominated. Not even a prize for special effects.

“Parks and Recreation”

Over a seven-year run, the fictional town of Pawnee, Pennsylvania was arguably the funniest locale on the prime-time map. And oh, what a cast! NBC’s workplace mockumentary included Amy Poehler, Chris Pratt, Rob Lowe, Nick Offerman, Aziz Ansari, Aubrey Plaza, and Rashida Jones.

In 2012, Time magazine cited it as the best TV show of the year. In 2013, the Television Critics Association (TCA) awarded it with the organization’s top comedy honor. But Emmy wasn’t as impressed. “Parks and Recreation” came up empty after 14 nominations.

Ironically, some of that bad luck could be attributed to Poehler’s “Saturday Night Live” pal Tina Fey. A good chunk of the “Parks” run coincided with Fey’s “30 Rock,” which was a big Emmy hog (winning 16).

“My So-Called Life”

OK, it’s not like the 1994 ABC drama that launched the careers of Claire Danes and Jared Leto lasted long enough to chase down a lot of Emmys. It was so ahead of its time that it was canceled after just one season.

Still, many consider it to be the best teen drama of all time and that’s why its lack of Emmy love is such a bummer.

The show did at least collect four nominations, including a best lead actress nod for Danes, who would go on years later to win two Emmys for her performance in “Homeland.”

“The Good Place”

Throughout its celebrated four-year run on NBC, this gloriously offbeat afterlife comedy starring Ted Danson and Kristen Bell, was praised to high Heaven by critics for its writing, acting and originality. It even won a Peabody Award and three Hugo Awards.

But Emmys? Nada. The show was nominated 14 times — including twice for top comedy series for its third and fourth seasons. Not even Danson could break through, even though he received three nods for lead actor in a comedy.

Other Emmy also-rans

These shows also failed to win a single Emmy: “The Leftovers,” “Veronica Mars,” “Happy Days,” “Parenthood,” “Good Times,” “Hannibal,” “Oz,” “Superstore,” “It’s Always Sunny in Philadelphia.”

Winners, but barely

Two other beloved series — “Buffy the Vampire Slayer” and “Gilmore Girls — did manage to break through, but not in a big way. “Buffy” (14 nominations) won twice in 1998 — for music and makeup. “Gilmore” was nominated just once and won in 2004 for makeup.

Keep an eye on …

“Better Call Saul.” AMC’s “Breaking Bad” prequel has been showered with critical praise, especially for its writing and the exceptional performances of Bob Odenkirk and Rhea Seehorn. But it soon will be going into its final season with 39 nominations — and no wins!