OP, you're right...opening credits are becoming a lost art. It's a shame, because I love a good opening titles sequence. But, ya know, gotta save time for more commercials.
One of the all-time greats: The Prisoner. Especially for its time, it's fast, aggressive, and without a word, tells the backstory of how Number 6 found himself in The Village. It also creatively mixes a thunder sound effect with Ron Grainer's music.
Also:
The Avengers -- This contains both the open and close, because the music in the close frankly rocks! Posed entirely in a studio, done partially in silhouette, this captures the cool, British nature of the series very well.
"The Prisoner" was the very first which crossed my mind - and you got there first in mentioning it; fantastic opening sequence, very well shot, great music and explains how No 6 found himself in The Village. One of my all time favourite shows.
Loved The Avengers, too.
Miami Vice was good, and earlier, Ironside had a very good intro, too.
