^You mean a "Very Special Episode" intro? Or generally "Tonight, on [Show Title]" announcements before the show? No, I don't think that's really done anymore, except as voiceovers on the end credits of the immediately preceding show. Everyone wants to get into the story as soon as possible, which is why Castle always puts its main title card off until a quarter of the way into the episode.
The "very special" thing. "Tonight, on a very special Cosby Show,
Dr. Huxtable gets cancer!"
To your other point, yes, the cold open is nearly ubiquitous these days. Networks now do their "tonight on..." promos over the credits of the prior ending show. Highly serialized shows still do "previously, on..." though.