The 1980-81 cast was intentionally comprised of actors meant to be reminiscent of the original Seventies cast. (Unfortunately, this gimmick ended up having a negative effect, particularly after the first sketch of the season was centered around it. The actors failed to live up to the comparisons in many ways.)
Gilbert Gottfried = John Belushi and Harry Shearer - Although, Jean Doumanian wouldn't actually allow Gilbert to use his manic personality that would've fit the Belushi comparison, and the Shearer comparison is a complete fluke.
Gail Matthius = Laraine Newman — Most obvious in the first episode, where Gail appears as both the Update correspondent and a valley girl.
Eddie Murphy = Garrett Morris — A comparison Eddie resented bitterly.
Joe Piscopo = Dan Aykroyd — Even adopting Aykroyd's Tom Snyder impression and motormouthed pitchman character.
Ann Risley = Jane Curtin — Bizarrely, Ann is stated in the opening sketch to be similar to Gilda... which is completely wrong. Going beyond SNL, she also came across as a Poor Man's Substitute for Diane Keaton, which makes sense since she was a Woody Allen protégé.
Charles Rocket = Chevy Chase and Bill Murray — Close enough to the latter, in fact, that Bill mentioned it in the episode he hosted that season.
The next cast (hired to replace most of the above) seemed to move away from the 'Seventies counterparts' idea, thankfully. For example, none of the original cast are particularly similar to either Robin Duke or Tim Kazurinsky.
Some members of the cast from the late 2000s to early 2010s are expies of previous cast members:
In 2013 members of the comedy troupe Good Neighbor (performers Beck Bennett and Kyle Mooney and filmmaker Dave McCary) joined SNL and were very clearly intended to fill the void left after the members of The Lonely Island departed, including making short films (though they're very conspicuously NOT labeled as Digital Shorts). At one point they seemed to be grooming Bennett to be an expy of Jason Sudeikis (versatile guy-next-door type), but he's ended up being much more like Chris Parnell 2.0, doing voiceovers and alternating in sketches between pompous and skeevy characters. He even took the Parnell role when Natalie Portman did a sequel to her rap with The Lonely Island.
Later on, comedy group Please Don't Destroy were added to fill Lonely Island's niche.
After Phil Hartman left they hired Michael McKean to explicitly fill the "utility player who can do impressions, leads and supporting roles and is a little older than the rest of the cast" slot that Hartman left open. But McKean's strengths were different than Hartman's, he seemed out of place and a bit uncomfortable in sketches, and he only lasted one and a half years (from the second half of the 1993-1994 season to the much-maligned 1994-95 season).
(performers Beck Bennett and Kyle Mooney and filmmaker Dave McCary) joined SNL and were very clearly intended to fill the void left after the members of The Lonely Island departed, including making short films (though they're very conspicuously NOT labeled as Digital Shorts). At one point they seemed to be grooming Bennett to be an expy of Jason Sudeikis (versatile guy-next-door type), but he's ended up being much more like Chris Parnell 2.0, doing voiceovers and alternating in sketches between pompous and skeevy characters. He even took the Parnell role when Natalie Portman did a sequel to her rap with The Lonely Island.