The Godfather: Part II: Frank Pentangeli was a replacement character for Peter Clemenza.
The Godfather: Part III: Tom Hagen is written out (died in between sequels) and is replaced by the much less charismatic and interesting George Hamilton character, B.J. Harrison. This was done thanks to a paycheck dispute with Robert Duvall, forcing Francis Ford Coppola to create this new replacement from scratch.
Lt. Mauser replaced Capt. Harris in the 2nd & 3rd Police Academy, acting as that film's villain and having more or less the same traits has Harris had, filling the same role. They were so similar that when Harris returned in the 4th movie, he was paired of with Mauser's assistant, Proctor, and the two had the same relationship Mauser and Proctor had.
Also, when Steve Guttenberg refused to reprise his role as Sgt. Mahoney for the 5th and 6th movies, Commandant Lassard's nephew Nick was brought in to fill Mahoney's shoes, while the 7th movie had a cadet named Kyle Connors also fill the very same spot.
When the Wachowski siblings wrote the second and thirdMatrix films, they originally intended to bring back the character of Tank from the first one. But after they had a falling-out with his actor, they created Link as a replacement.
Roman in 2 Fast 2 Furious replaced Dominic from The Fast and the Furious as the Anti-Hero with a criminal past. Though it's worth noting that Brian is now the main character with Roman as his sidekick, instead of co-lead with Dom. Both Roman and Dom are back in Fast Five.
Beerfest plays this one for gags, when Landfill dies and the character is promptly replaced by his twin brother, portrayed by the same actor, who asks the rest of the characters to refer to him by his dead brother's name and never speak of the death again. He then promptly sleeps with his dead brother's widow and "feels that he's already known them all his life."
A rather bizarre set of examples occurred regarding the monster Baragon. First, Destroy All Monsters was going to have Baragon be the monster seen destroying France. Unfortunately, the suit was too badly damaged and instead Gorosaurus was used (Ironically, the dub version still calls Gorosaurus "Baragon")...And Baragon himself was reduced to a mere 10 second cameo. Later, Baragon was going to appear in Godzilla VS Mechagodzilla but the suit was still too damaged to function and Anguirus was used instead. In both cases, Anguirus and Gorosaurus were given traits that were originally attributed to Baragon (IE: Jumping and burrowing).
Godzilla vs. Space Godzilla was going to have Godzilla team up with the human-built Mechagodzilla previously seen in Godzilla vs. Mechagodzilla II to fight SpaceGodzilla, but Toho realized that having Godzilla fight alongside the machine that came close to killing him would make the battle against the new villain too one-sided. Instead, they brought in M.O.G.U.E.R.A., another human-built robot that had also been controlled by alien invaders when first seen in its Showa era incarnation.
The spinoff Rebirth Of Mothra trilogy apparently knew it wanted to save KingGhidorah for the role of the final film's antagonist, but also wanted to draw audiences into the series with a villain of comparable menace. The first film's solution? The totally original, terrifying, powerful, destructive, evil new monster... Death Ghidorah. ...Hmm.
Los Superagentes: Nueva Generación. Unlike the sequels to Bañeros and Brigada Explosiva, the new characters were clearly meant to replace the originals, as per the original Tiburon and Delfin show up in insultingly short cameos as opposing to joining in the action. Worse, the original Mojarrita and Chief of Acuario don't even show up.
Jason replacing his own mother as the slasher in the sequels with the same M.O. and a related motive.
Roy Burns from Part V (Following Jason being "Killed Off for Real"... for one film) would be a more "traditional" example. When disguised as Jason, Roy not only used his M.O. but also acted like Jason; silently determined instead of deceptive, crazy-violent and motive-hissing.
When Crazy Ralph was killed in Part 2, audiences were introduced to very similar doomsayers in Part III and VIII.
Subverted like no tomorrow in Scream 4. Characters are thrown at us as being replacements for the characters of the original film, but most of the new characters die, the apparent Sidney replacementturns out to be the killer, and we even get a subverted Billy replacement who is almost successfully framed for all the murders.
Every Cenobite that follows Pinhead that is NOT Butterball, Chatterer or the Female Cenobite in the Hellraiser sequels.
Due to not having a high enough budget to render the characters' powers onscreen, Husk and Chamber were excluded from the Generation X TV movie and replaced with Buff and Refrax, two new heroes who had similar, but cheaper abilities.
"Nigel" appears to be a replacement Composite Character for Colin and Dennis Creevey. (Colin appeared in the second film, but the actor decided not to do any more after that. Dennis never appears in the films full stop, but he's a very minor character in the books anyway.)
Star Wars: The Phantom Menace had Captain Panaka (Hugh Quarshie), Queen Amidala's bodyguard. After Quarshie was unable to make it to the location shooting for Attack of the Clones, he was replaced with Captain Typho (Jay Laga'aia). Aside from the eyepatch, they're the same, both in appearance and personality, to the point that some viewers wondered why Captain Panaka was suddenly sporting an eyepatch.
Rock Star depicts such a replacement when the main character Chris, lead singer of a tribute band, is hired to replace his idol due to his intentionally similar appearance and slightly better vocals. The film culminates in Chris picking a fan out of the audience at a concert to replace himself. This is based on actual events: Judas Priest replacing their original lead singer by picking the front man of a Priest tribute band.
In The Room, the actor who plays Peter (essentially the voice of reason or the man who "is always playing psychiatrist") quit at some point during the shooting. Another actor replaced him and took the lines he would have had in a later scene. However the new character never has any formal introduction. It is just implied he is another friend.
Duke is a suspiciously similar substitute for his deceased identical twin Curly. Granted, his personality is different enough (less of a Jerk with a Heart of Gold, more Machiavellian) not to be cause for viewers to truly cry foul (there are shades of the Evil Twin trope here), but he's a suspiciously similar substitute all the same.
Bruno Kirby did not return from the first movie, so his spot was filled by Jon Lovitz, playing Billy Crystal's annoying brother.
Quarrel Jr., in Live and Let Die is a Suspiciously Similar Substitute for his father, Quarrel, who was killed in Dr. No. This is because the films were made in a different order from the books, where Quarrel gets introduced in Live and Let Die, before being killed in Dr. No.
Also, Megan Fox's Mikaela being replaced by Rosie Huntington-Whiteley's Carly.
In the second Rescuers film (which takes place in Australia), the role of Orville Albatross is replaced by that of his brother, Wilbur.
The Third Stooge. While Shemp was not Suspiciously Similar, Joe Besser and "Curly" Joe DeRita were. All three of them had their own unique method of delivery, however, distinct from Curly.
When George Sanders grew tired of appearing in The Falcon movie series, it was decided that his Gay Lawrence character would be killed off. The series continued with Gay's brother Tom stepping into the role of the Falcon. Tom Lawrence was played by Tom Conway ... who just happened to be George Sanders' brother.
Averted in the remake of Shaft. Samuel L. Jackson didn't want to step into the iconic character's shoes, so the character was written as John Shaft's nephew who also happened to be named John Shaft. This seems to hang on one line of dialogue until Roundtree shows up in a cameo as the elder Shaft. Jackson's character is therefore not a Suspiciously Similar Substitute, but he does invite Counterpart Comparison.
In The Mighty Ducks, Coach Bombay's mentor is his late father's old friend, a kindly Norwegian sporting goods vendor named Hans. In the sequel, he is replaced by his brother Jan, who makes an offhand comment that Hans is visiting their mother in Norway. Then, in the third movie, Hans has returned, and Jan is nowhere to be seen—he doesn't even show up at Hans's funeral.
The Death Race prequels star Luke Goss as Carl Lucas, rather than Jason Statham as Jensen Ames. Like Statham, Goss is a white British man with a shaved head and Perma Stubble. The characters aren't hugely similar, but appearance-wise they're very much alike.
Most of the The Texas Chainsaw Massacre 1974 follow-ups introduce new family members who are similar to Drayton and Nubbins, Leatherface's brothers in the first film.