Watching some old shows on Blu-ray with original bumpers got me thinking about shows with commercial bumpers built directly into the show.

Hawaii Five-0 - The giant wave
Mannix - picture divides into squares which disappear one by one, then reappear in reverse.
Man From U.N.C.L.E. - picture freezes and goes out of focus
Thriller - white lines appear on screen like a web
Wild Wild West - picture freezes and becomes one of four corners
Lost in Space - although the "Continued next week" had been discontinued they did it once per episode in the same manner during season 3

What show had the picture break up like a jigsaw puzzle? Get Smart?

That's all I can think of.

Wasn't there a cop show that came back from commercial break with a title card like Act III: The Missing Unknown?

MST3K had the silly-string planet.
Sixty Minutes had the stopwatch.

G1 Transformers cartoon

The new MST3K even continued doing bumpers with voiceover by Patton Oswalt, despite being commercial free.

24 - had the clock

We now return you to the Transformers. I can still hear that line read in that very distinctive voice they used in my head, after all these years.

I thought about shows with titles for Act I, Act II, etc. but not sure if they are really bumpers or just titles.

Thought of another one, The Untouchables.

All "Quinn Martin Production"s (and that credit was always spoken in the title sequence) had "Acts". His shows include "Barnaby Jones", Cannon", "The F.B.I.", "The Invaders" and "The Streets of San Francisco".
There was also an "Epilogue".
A lot of these things have gotten lost with editing for syndication.

"Hill Street Blues will be right back."

"Charlie's Angels" would lead into commercial beaks ("act breaks") with a music cue (a few bars of the theme) and a fade-out (or the screen went out of focus, -I forget).

All shows had that. That would be a regular bumper. If the music or other audio from the actual show continued in the background it would be built in.
With Hawaii Five-O the music builds, continues while they show the wave, then the wave and music fade out together. The wave could be edited out but the music would be cut short.

A regular type bumper that is rare to see from classic shows is

"The following program is brought to you in living color" with the NBC peacock. For the first couple years most shows had a "in color" bumper at the beginning. Still see it on Batman episodes. Rat Patrol had it in the title so still see it.

Anyone remember,
"(blank) will not be seen this week so we can bring you the following special presentation"

Are we talking classic shows only, or do contemporary shows count?

If so, then NCIS definitely has them. At the start of each act, there is a black-and-white freeze-frame or near freeze-frame shot, accompanied by a signature sound effect. This is unofficially known as the "foof" of the act, and typically represents the final shot of that act. It is bookended by the same shot at the end of the act, again fading to black-and-white.

As a trivia note, the "foof" sound effect was originally created by producer Donald Bellisario striking a microphone with his hand.

That would count

As I remember, the 1963-66 sitcom "The Farmer's Daughter" had bumpers. The show was about a Swedish girl who becomes a nanny for a politician. When they would break for a commercial, they would have a picture of star Inger Stevens with the text "The Farmer's Daughter will be right back after this commercial" while Stevens read the text in Swedish. (My memory is a little foggy here).