Opening titles are supposed to transport us to the time and place of the story we are about to see. Original Dallas did this beautifully, the sweeping views of the Dallas skyline transitioning to the ranch let us knew this would be an epic story with larger than life characters. The theme with its elements of old country fiddles, echoes of Aaron Copland and disco rhythm let us know we are in the present but there is a strong sense of history to this story.
As networks turned more time over to ads, which resulted in episodes becoming shorter, producers decided to shorten or eliminate opening title sequences. I think this is a mistake. We don't necessarily need the premise of the story told to us (something Sherwood Schwartz liked to do) or presented visually (which Bewitched and I Dream of Jeannie did) but I think an opening can help the viewer transition into the world of the show/movie, especially with stories that are larger than life or set in a world that is far removed from our everyday lives (either historical or fantasy). Imagine The Twilight Zone without its iconic opening or Gone With The Wind without it scenes of the antebellum South and the film's title scrolling across the screen as if it is being blown by the wind.
One of the best openings of all time (imho) is Superman: The Movie. It starts with a theater curtain pulling back to 3:4 aspect ratio, we see black & white footage of a Superman comic book as a child tells us who Superman is. Then the curtain pulls back the rest of the way to wide-screen, the footage changes to color and the titles whoosh through the stars as we fly to Krypton. This is how you start a movie:
I totally agree, tv shows now are really missing a trick by skipping a decent intro, don't get me started on Home & Away! One of the most well known tv themes out there and they don't bother using it properly, such a waste. I am glad when they bought the X Files back a few years ago they did not cut the opening titles and infact reverted to the more popular and recognisable ones of the shows early years, it worked!
I loved the way original Dallas altered the arrangement of the theme slightly each year whilst it was clearly still the same loved tune, it kept it fresh and dynamic, no matter how many times I watch Dallas, or Dynasty for that matter, I could NEVER skip the titles, the episode would feel incomplete.
Imagine The Twilight Zone without its iconic opening or Gone With The Wind without it scenes of the antebellum South and the film's title scrolling across the screen as if it is being blown by the wind.
Or imagine Quinn Martin shows without the announcer saying that what you were seeing was "A Quinn Martin Production," and then aurally billing the star(s) of the show, and guest star(s) for that particular episode.