A while back I made, but never got around to doing anything with, some 20-to-30-second "condensed" versions for intros from older TV shows. The idea was to see if I could get as much of the gist of the original sequence as possible while keeping it under 30 seconds (since no show today, except on premium cable, is permitted to have an intro that's longer than 30 seconds).
All I discovered, really, is that a longer intro is usually more effective than a short one. And we already knew that. But the one that I thought worked pretty well was The Rockford Files: with just the answering-machine message followed by the last few notes of the theme song, it has the most important part of the intro intact and still has musical punctuation for the joke.
I also tried to come up with a short Laverne And Shirley that would keep the most important bits from the intro (the introduction, Lenny and Squiggy, the glove, the girls looking dreamy, the girls running off to work) while shortening the theme song and, in the modern fashion, putting the show title at the end.
I also tried to do a really short Mary Tyler Moore, shorter even than the shorter title sequence that they sometimes used on the actual show. This is just too short for it to make any sense, I think. I sometimes feel like a show would be better off having no title sequence rather than a 15-20 second one; it just feels like a buildup to something that never comes.
Other older shows, like Bob Newhart, actually alternate intros that ran 30 seconds or a little more, which they would use in episodes that ran long (so they could take time out of the main title instead of cutting the episode proper). And other shows actually did have very short intros, like The Dick Van Dyke Show.