As much mournful as ominous, the words in the opening credits (in all TV airings on UK television, and from Season 2 onwards in the U.S.) are actually a Sanskrit prayer known as the Gayatri Mantra, considered to be the holiest verse in the Vedas, the founding texts of Hinduism. Roughly translated into English it reads:
Oh God! Giver of life, earth and sky That heavenly light which must be worshipped Let us attain the radiance of God May our thoughts bring us ever forward into light
Baltar also listens to a hilarious Italian opera way back in the first season:
Woe upon your Cylon heart. There's a toaster in your head. And it wears high heels. Number Six calls to you. The Cylon Detector beckons. Your girlfriend is a toaster.
"Kobol's Last Gleaming" from the Season 1 soundtrack contains proper Latin chanting, using the words "Ita Dicimus Omnes", "So Say We All".
Buffy the Vampire Slayer has this. Usually, though, it isn't so much chanting as speaking it to perform spells and/or do rituals.
In one particular case in Season 2, it was ominous Italian opera when Giles discovered that Angelus had killed Jenny Calender. The moment is also another Whedon example of Anyone Can Die
While good characters are shown to use magic in the show, as a rule the good guys (okay, 'girls') cast spells in what is actually intentionally-badly-pronounced Italian (so it sounds ancient), whereas the bad guys e.g. Warren use Latin chants.
The straightest example of this comes in a flashback when the still human Drusilla enters a church for confession, and is encountered by Angelus who just ate the priest. The background chorus sings ''Pange Lingua'', an old eucharist hymn, presumably from The High Middle Ages, with some variations.
The Japanese gameshow subtly titled Cat Weightlifting includes hints of Ominous (probably Japanese) Chanting when the scientists are placing the final fish on the ground. The show also features unnecessarily awesome music when the cats manage to escape with the increasingly larger fish, and some Metal when each cat gets knocked out in the final round. If you've no idea what it's about, go watch the video already.
For the most part in Charmed, practitioners of Good Magic cast spells in English Rhyme, whereas Dark Magic was done in Latin.
The mini-series Chernobyl concludes with a montage, explaining the fates of the people depicted in the show to the track, Vichnaya Pamyat, or "Memory Eternal"; an Eastern Orthodox funeral hymn.
"In a blessed falling asleep, grant, O Lord, eternal rest unto Thy departed servants and make their memory to be eternal."
The Atlantean cult in "The Underwater Menace" chant ominously in a gibberish language ("waa-aa-tuu-aah waa-aa-tuu-aah Wah! Wah! Wah!") while performing religious rituals (like chaining the Doctor and his companions on top of a shark pit). It is combined on the soundtrack with dissonant electronic hits and a creepy organ.
"Bad Wolf": The first appearance of a massive Dalek army is accompanied by Ominous Hebrew Chanting. (The words are reported to be a translation of "What is happening?", which apart from being an appropriate response to the situation is also a Dalek Catchphrase.) The words are "Mah Koreh, Mah Mah Koreh" (what's happening, what, what's happening) repeated over and over again. Here is the theme.
"Tooth and Claw": The bald monks chant "Lupus Deus est" "the wolf is god" as the Moon rises.
A moment in "Doomsday", featuring the use of the Daleks' Genesis Ark sending millions of Daleks against the 5 million Cybermen that have already taken over the world winds up using the prerequisite chanting as well.
The theme for S2 of Fleabag. In a bit of Bilingual Bonus, the Latin is made up of words for the genitalia and sexual congress.
A Left the Background Music On variation when Frasier goes to Bebe's hotel room and there's a choir singing outside the window. While she tries to seduce him, he throws open the window to get some air just as the choir hits a particularly ominous crescendo, accompanied by sweeping red floodlights.
Hannity's America on Fox News has been known to use Carmina Burana as a cold opening sometimes, usually to a montage of "sinister" goings-on amongst (usually) Democratic political figures in Washington, D.C. Apparently it's supposed to be funny, although Hannity's America is generally serious.
Another "hard to tell if it's Latin or not" but the Highlander: The Series episode "The Immortal Cimmoli".
Parodied on How I Met Your Mother. When Barney pressures Ted to swear an oath to him as his bro (a "bro oath" or "broath"), he lends the ceremony some extra solemnity by playing a recording of some chanting monks. It takes Ted a couple minutes to realize the monks are actually just chanting the word "bro" over and over; Barney had them record it just for the occasion.
Happens on the original Japanese Iron Chef, whenever the Iron Chefs rise to the stage.
Played with in Kamen Rider Faiz in which a Corrupt Corporate Executive (though to be fair, the entire organization was corrupt too) played this chanting on a personal CD player in his office whenever he was on the job. The situation didn't matter; he could be planning world domination or just relaxing after a hard hour's work, but the Chanting would still be belting out at full volume. Thanks to the show having a serious tone 99% of the time, this came off as more creepy than humorous.
The soundtrack for Lexx includes a fair amount of random choral chanting (although a lot of it is just oohs and aahs).
The miniseries adaptation of The Master and Margarita has Ominous Latin Chanting out the wazoo, with a few "abracadabra"s thrown in for good measure. "Woland's Hymn" is the most prominent example.
Sator arepo tenet opera rotas Igni natura renovatur integra INRI, INRI, abracadabra...
Ominous Chanting is quite common on Merlin, though it's so indistinct that it's hard to tell whether or not it's Latin. Or what they're saying. It's very old English according to the DVD extras.
In The Middleman, when Sensei Ping does the Wu-han Thumb of Death, it's accompanied by the "Dies Irae" from the Mozart Requiem (along with stock footage of Stuff Blowing Up).
A Running Gag in the game show Pointless is that the hosts will imitate Ominous Latin Chanting whenever a round goes to a tie-break.
The theme to the darkly humorous Danish television series Riget (of which Stephen King's Kingdom Hospital is a remake) mixed genuine Latin phrases with gibberish, counting to seven in English and slow spelling of the word "rectum" . Even the legitimate Latin is nonsense ("speculum et cetera"; "mirror and so forth").
Star Trek: Picard: In "Broken Pieces", when the Zhat Vash initiates prepare to face the Admonition, chanting in a mysterious language (possibly Romulan) can be heard. On the soundtrack, the music is called "Tal Shiar Admonisher".
Same goes for Supernatural with its various exorcisms and rituals, not only in Latin, but sometimes even in Enochian.
Even Survivor (yes, the reality show) has done this with a generally unliked contestant (somewhere between quirky, insane, and power-hungry) doing yoga in the rain (complete with ominous lightning and thunder) as "O Fortuna" plays in the background.
Sweet Home has ominous Korean chanting when the situation looks especially grim for the survivors, including when Hyun turns into a monster.
In the Teen Wolf episode "The Girl Who Knew Too Much", both Ominous Latin Chanting and "Psycho" Strings appear as the season's villain takes another sacrifice and attempts to kill a main character. This is amplified by the fact that the intense scene takes place in the school classroom while a recital takes place elsewhere in the school, and the Psycho Strings and Ominous Chanting are actually real in the universe, with the performers in the recital doing both. It is implied that the villain was able to possess the choir and orchestra to do this, simply because she has a flair for the dramatic. This supposed possession is actually the cause of death for the villain's victim—the pianist pounds on the piano keys so hard that one cord snaps and slashes her throat.
Spoofed in A Touch of Cloth III, where the sacrifice cult is accompanied by this kind of music, but the lyrics are just inane things like video game titles, brand names and politicians ("ESTEÉ LAUDER!" "SUPER MARIO!" "DAVID MILIBAND!")
Vikings has ominous chanting, only it is in Old Norse.
Warehouse 13 's pilot had Ominous Medieval Italian Chanting.
Once a player goes to the third level ($50,000 and beyond) on the game show Who Wants to Be a Millionaire?, the background thinking music starts to sounds more and more dramatic, with a choir chant playing over top of the music. However, the background music for the $1,000,000 question is a complete subversion, instead consisting of just a low, deep bass note, a drum hit, and a heartbeat.
In the Discovery Channel series Wild Tropics, whenever the sharks or other dangerous predators show up the music shifts to Ominous Polynesian Chanting.
Lampshaded in the The Young Ones episode "Flood", where a group of monks walk by chanting "Dominus ad nauseam, dominus ad nauseam..."