Before reality tv, and before Shondaland, your go-to for an evening of trashy, soapy escapism were the glitzy evening soaps. Knots Landing, Falcon Crest, The Colbys, Dynasty, Dallas. For the most part, these shows weren't trying to be aspirational, you were never going to be rich like them. It was pure Reagan-era, Greed Is Good wealth science fiction. Now, nothing will beat Dallas for overall cultural impact, JR Ewing is an all-time hall of fame villain and "Who Shot JR?" is a top 5 TV cultural event (Non News Category).
But Dynasty had the better opening, mostly because of the theme music, especially the killer horn flourish right at the end. It had that kind of British-ish feel that classed up the joint, in the era before TV producers realized they didn't have to pay real actors like Diahann Carroll and Joan Collins real money to mud wrestle or whatever on camera, when they could get an endless pool of college students to do it in exchange for tequila shots. Nearly every member of the cast in the opening credits looks just one volcano lair short of being a Bond villain (except for Pamela Sue Martin. I have no idea what acting choice she thinks she was making in her opening credits shot, or why the producers kept it. Dull Surprise indeed).
2. The Equalizer.
If Dynasty is Reagan-era affluence fantasy Metropolis, the opening of The Equalizer is Reagan era Gotham. This opening is scarier than the opening credits of actual horror shows, it's a world full of poorly lit streets, grafitti and muggers and rapists and suspicious ethnic minorities, an incredibly precise distillation of at least pre-9-11 conservative fear politics, all set to a driving, heart racing off balance synthy score. Happily there's an old white guy here to fix it! I will say though, for the lady trapped on the subway platform, that dude mostly looks like he's your manager disappointed you didn't put a cover letter on your TPS reports.
3. All in the Family.
TV shows have different types of opening. One of them is the catchy opening song (Non-Expository). And of course this is one of the all time classics. Two middle aged folks, affectionately/regretfully singing about when everything made sense. It's the gentle song version of Abe Simpson's "I used to be with it, but then they changed what *it* was." speech. Or the gentle song version of the second season of The Wire. Also the song that indirectly taught me what the hell a LaSalle (and from there, many other now defunct brands of car) was.
4. Uchuu Senkan Yamato/Space Battleship Yamato/Star Blazers.
And here's one for catchy opening song, expository. The Japanese and English versions of the theme song have different lyrics (the English lyrics go into more specific story detail), but the sentiment is roughly the same: Earth is dying (due to nuclear bombardment by evil aliens), we're leaving to go on a long voyage to save her (via a good alien ally who can give is Earth-fixing tech if we can reach her home planet), we're sad but also brave and hopeful we can return and save the ones we've left behind.
Obviously there's a ton of stuff here about Japan's post-WW2 attitude towards the military and nuclear weapons, I mean, the ship that's going to rescue the human race is literally the WW2 Yamato, repaired and extensively retrofitted (with the help of some alien technology) to be a spaceship, and this song has been regularly played by Japanese military bands.
I've linked the Japanese version from the recent, very good animated remake, Yamato 2199, mostly because the visuals for the new version are so good.
Simple. Dramatic. Just the facts, maam.
6. The Outer Limits
Okay, if I had to put only one "Creepy Sci-Fi/Horror Anthology Series" into the TV Show Hall of Fame, yeah, I'd go with The Twilight Zone. But I think the opening for the Outer Limits is cleverer and scarier. Of course kids today in a post-cathode ray tube world won't connect with the screen maipulation stuff (maybe that makes it even weirder and scarier).
7. Challenge of the Superfriends.
The Timmverse DC superhero shows were better, of course (Batman the Animated Series, Justice League/Unlimited, etc). But for pure "Here's my pile of action figures on the living room shag carpet, the fight choreography is mashing good guys and bad guys together while making "Chrsshsh! Pwoosh!" noises.", nothing beats this. THE JUSTICE LEAGUE OF AMERICA, VERSUS THE LEGION OF DOOM. Bless Ted Knight's narration, and the amazing score.
8. Miami Vice
ER changed the way we think about pacing on TV shows. Miami Vice made us change the way we thought about the use of popular music to inform the narrative. Nothing looked like Miami Vice, and nothing sounded like it. If you can, I highly recommend tracking down the last episode of the show, they do a flashback/montage of various scenes from the show and some of the shots are utterly stunning. Also, while I stand by this choice, I think you can't mention it without acknowledging its spiritual parent: https://www.youtube.com/watch?v=uQ9xfNn
9. Babylon 5, particularly seasons 1-3.
Babylon 5 was an early, ambitious exercise in long form storytelling on TV. Each season had a different opening reflecting or explaining the current state of things in the Bab5 universe. The openings of seasons 1-3 in particular condense things down to one tragic narrative arc: Babylon 5 was built to prevent war... and it failed. Grim stuff, especially for the time. Excellent music from Christopher Franke, groundbreaking for the time graphics.
10. Misfits of Science.
Short lived, largely forgotten show, fine. But the intro is so much fun (there were surprisingly few superhero TV shows in the 80's), and the intro song is like some perfect piece of 80's New Wave beamed in from an alternate Earth where the show was super successful. Hi, super adorable, just slightly post-Dancing In The Dark Courtney Cox!
Honorable mentions: Any show with opening music by Mike Post. Any opening of a show produced by Glenn A Larson.