It seems as if a lot of English actors showed up on Midsomer Murders ( if only until they died), and I’ve seen more than a few famous faces on Perry Mason, such as Harvey Korman and James Coburn. Any other shows that had a lot of pre-famous recognizable actors?
The Twilight Zone.
Chris Pine had his first credit on ER. Zac Efron had his second. Eva Mendes had her third. And tons of other actors were folks with only lists of single appearances in other shows - Shia LaBeouf, Rooney Mara, Eric Stonestreet and Lucy Liu. There were probably more.
Law and Order, somewhat famously.
The Australian soaps Home and Away and Neighbours churn through young talent. Chris Hemsworth and Margot Robbie are just some of the recent alumni, along with Craig Pearce
The argument about why Australian actors are well-regarded in Hollywood is that these soaps give you excellent training. A lot of Home & Away especially is filmed outdoors on beaches - the expectation is that if you are a young hunk or starlet you will turn up on time, know your lines and not waste time on multiple takes before the sun goes, and you are not special and will not be treated as such.
The Love Boat had a large number of guest stars per episode, and thus many many well known at the time and wellknown later folks
We recently burned through Marple (2004-2013) on Amazon Prime. It was a cavalcade of recognizable British names.
A friend of mine from acting school twice played the nameless opening witness, a couple seasons apart (“I was just walking by and saw the body in the bushes / heard the noise in the alley / etc”). Just a nice generic urban face, I guess.
And Third Watch, which can be found alongside Law and Order in just about every middle-aged stage actor’s Playbill bio.
I was going to add: Perry Mason.
Tripler
I wish I knew how to type his ‘catch tune’ with the crescendo of horns & strings.
The Outer Limits. The original had upcoming actors William Shatner, Robert Culp, Robert Duvall, Ivan Dixon, Edward “Chief” Platt, Dabney Coleman, Martin Landau, David McCallum, Leonard Nimoy, Carrol O’Connor, Sally Kellerman, James Sikking, Donald Pleasance, Adam West, Nick Adams, Barry Morse, Martin Sheen, Grace Lee Whitney, Bruce Dern, et al. (I’m not listing actors who were established before the show)
The downside of looking people up on Prime when I see them is that it doesn’t list everything they’ve done, so I don’t know if they’re on Perry Mason early in their career or if it’s after they’re well-known.
FWIW, The Wild Wild West had a metric tonne of guest stars that were on Star Trek, as these lists will attest:
Granted, many of these were bit players passed around from show to show.
This is just for ST; many other actors on WWW were in other movies/TV shows.
In just the three seasons I’ve seen of Columbo so far, they’ve got recognizable actors in super small bit roles.
Marc Singer as a doctor on TV.
Barbara Baldavin as a secretary with like two lines
The woman at the beginning of Stripes. The one whom Bill Murray abandons in a cab. Has like one line in an ep
Anitra Ford has ZERO lines in one appearance.
I know these arn’t particularly famous people but recognizable for sure.
You mean from, “Invasion of the Bee Girls”? Or that daytime game show… what was that called? 
It seems that any time I look up an English actor, I find out that they were in The Bill.
The Wikpedia entry even has a section dedicated to Notable guest stars.
Emergency! has John DeLancie as a San Francisco-based doctor. His character is a bit of a jerk, as I recall.
Others I recall on Emergency!: Deidre Hall, Donny Most, Laurette Spang (pre-BSG), Anne Lockhart (also pre-BSG)Sharon Gless, Larry Storch, Dick Van Patten, Ruth Buzzy, Michael Conrad, Jamie Farr, Mort Sahl, Bruno Kirby, Vic Tayback, among many others.
There was also “stunt” casting like Mark Spitz and his wife, Kareem Abdul-Jabbar, and other atheletes.
Gunsmoke must be a top contender, having run for 20 something years. According to MeTV.com, 60 young actors who later went on to greater fame appeared on the show:
Just as Twilight Zone had lots of “before they were famous” actors, the two Alfred Hitchcock anthology series had many as well. Just yesterday I watched the hour episode Memo From Purgatory (3.10, 1964) with James Caan and Walter Koening, plus future studio head Lynn Loring.