But appeared in a huge chunk of the show. So basically if you had a first episodes and last episodes marathon, these actors/characters would not appear.

For example...

Khandi Alexander played Catherine Duke on "NewsRadio" from episode 2 to 60 (and guest starred in episode 76) of the 97 episode series.

Sasha Mitchell played Cody Lambert on "Step by Step" from episode 4 to 112 (from late season 5). He reappears once more in the second-to-last episode... but that ain't the last episode! ;)

Lisa Robin Kelly played Laurie Forman on "That '70s Show" from episode 2 to 63 (from season 3). She reappears briefly late in season 5 but that's the last we see of her (LRK, that is. Laurie continues on for a little while with a different actress in season 6).

Now you name some!

Actually, Rue's first appearance on Maude was in Episode 9 of Season 1 - the 1st of the 2-part abortion storyline. Maude shocks Vivian by revealing that she's pregnant. She also appears in Episode 21 of Season 1 - where Vivian and her husband Chuck announce they're getting a divorce.

But it is correct that Rue fits the criteria of this thread, playing a character in a majority of the episodes of a series but not in the 1st or last episodes.

Betty Garrett appeared on "Laverne and Shirley" for 96 of the 178 episodes. She doesn't appear until October 1976 (show started in Jan. 1976) and stopped appearing in 1981 (show ended in 1983).

I've got one in mind, but it only counts depending on how you count episodes.
While Dana Elcar actually appears in the Pilot episode of MacGyver, he appears as a totally different character (Andy Colson). He doesn't appear as Pete Thornton until episode 11, "Nightmares". (He goes on to appear in many of the rest of the Season 1 episodes from there.) He then becomes a regular on the show from Season 2 until the final season, Season 7.
However, while Pete Thornton does appear in the series finale episode, "The Stringer", he does not appear in the last episode of the series aired, which is "The Mountain of Youth". So it depends on how you want to look at it for MacGyver. This show is one of those cases where the series finale episode actually aired first- and then later a "lost" episode was pulled out to air later in the summer, after the series finale did so well. So that may be really technical, but most episode guides still list "The Mountain of Youth" as the last episode because it's by airing order, rather than production order.

James MacArthur can be added to the list for the original Hawaii Five-O. Another actor played Danny Williams in the pilot episode, and James took over with the 2nd episode. Then, he didn't appear during the final season.

The following cast members of the TV show "Fame"(1982-1987):

Nia Peeples (1984-1987)
Janet Jackson(1984-1985)
Morgan Stevens (1982-1984)

Other shows:
Lisa Reifel who played Emily Weston (1992-1993) on Empty Nest.
Sinbad from "A Different World".
Cory Tyler of "A Different World".

James MacArthur can be added to the list for the original Hawaii Five-O. Another actor played Danny Williams in the pilot episode, and James took over with the 2nd episode. Then, he didn't appear during the final season.

The Hawaii Five-O pilot however did not air as the 1st episode. Season 1, Ep. 1 did have MacArthur in it. The pilot footage wasn't used until later that season.

From IMDb: "The series pilot, which originally aired as a two-hour TV movie, is re-edited as a two-part episode of the series." (emphasis mine).

http://www.imdb.com/title/tt0598024/?ref_=tt_ep_pr

It all hinges on whether a movie that preceded the series can be considered Season 1, Episode 1, which really it wasn't according to IMDb.

Sandra Kerns as Ellen Powell on "Charles in Charge" (as the syndicated seasons progressed, she showed up less and less- and since the Powells weren't around in the first season, she didn't show up in either the first episode or the last episode. However, since you could think of the 2nd. season as a rebeginning for "Charles in Charge", it's probably worth noting that she was present for the 2nd. Season premiere episode, "Amityville".)

Also, Justin Whalin's character on the show, Anthony.

Waldo Faldo from Family Matters. He made a cameo in a S1E16 as a nameless character and didn't officially become a character until mid-season 2. He was made a regular in season 4 but left after season 7, meaning he wasn't in the final episode.