Again, I'm sorry if this has been talked about already, but I did not find it.

Did any of the characters (Jack Tripper, Janet Wood-Dawson, Chrissie Snow, etc.) appear on any other shows, as parody, in-joke, reference, or whatever? And whether or not they were played by the same actors?

(Excluding, of course, Three's A Crowd and The Ropers.)

It seems Norman Fell played a landlord named Mr. Roper in one episode of one other show.

Did it ever happen with any of the other characters?

It seems Norman Fell played a landlord named Mr. Roper in one episode of one other show.

I think that show was the Fresh Prince of Bel Air

In 8 Simple Rules they do a 3's Co. episode where the kids are the trio and John is the landlord Mr. Roper. Very funny episode and impressive how the set and everything looks like it did in 3's Co. And to top it all off, John's character wakes up in bed with Furley!!!! Hilarious! If you wanna check out the show it is out on DVD.

Norman Fell Played Mr. Roper in Fresh Prince of Bel-Air and in an episode of Ellen.

"Ellen" .... Mr. Roper (1 episode, 1997)
... aka These Friends of Mine (USA: first season title)
- Roommates (1997) TV episode (uncredited) .... Mr. Roper

"The Fresh Prince of Bel-Air" .... The Landlord (1 episode, 1994)
- What's Will Got to Do with It? (1994) TV episode .... The Landlord