Below are the tiers in which I think a character's the most at risk. The order the characters in each tier are listed is not in any specific order.
Any characters that go unmentioned, I consider to more or less be completely safe.
Tier 1 (The likeliest cuts)
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Cloud (I think he's the most likely cut of them all, and I'm honestly surprised so many people here seem to think he'll be back for certain. The lack of content related to Final Fantasy in comparison to that of other third party franchises suggests to me that he had the most licensing difficulties, which does not bode well.)
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Lucas (I think the idea that a character "cannot be cut twice because it would upset people" is silly.)
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Roy (See Lucas. I'd like to add that I see him as being every bit a risk as Lucina, in spite of being far more unique than she is. Derivative characters and clones have proven to be likely cuts in the past, and I don't see that changing. After having strongarmed her into FE Warriors, I can see Intelligent Systems rescuing Lucina. Roy's greatest advantages are Melee nostalgia and apparent popularity in the FE Heroes polls.)
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Lucina (I think the idea that the costume clones are safe just because they're low effort is a bit flawed; the Melee clones were also low effort, and they ended up comprising the entirety of Brawl's cuts except Mewtwo.)
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Dark Pit (See Lucina)
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Dr. Mario (See Lucina AND Lucas)
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Tier 2 (Less likely, but still at risk)
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Mewtwo (See Lucas. I put Mewtwo on a tier above the other returning cuts because he's significantly more popular than they are, and has a unique moveset. The fact that he was low enough priority to get cut in the first place, and then failed to get into the base version of SSB4, however, is quite telling.)
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Bowser Jr. (A lot of people seem confident about him returning, but the fact that Sakurai singled him out as a character who was on the chopping block in SSB4 raises concern. The 8-characters-in-1 dynamic also gives him quite the workload.)
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Ryu (He's here mostly because he's a third party. Even though he's more important to Capcom than Mega Man is in recent years, the fact that Mega Man was on the base game of SSB4 and Ryu was DLC suggests to me that if one of them were to be cut, Ryu would be the one we'd be saying "bye" to.)
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Tier 2.5 (The Wildcards)
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Mega Man (Third party status. I don't think any of them should be considered safe. As mentioned in Ryu's section, the reason I put him on a tier below him is because he was part of SSB4 from the beginning, while Ryu was post-launch DLC.)
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Pac-Man (I think his likelihood is dependant on whether or not Bamco is returning to develop this game. He's a bit less likely if they're not, and significantly more likely if they are.)
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Tier 3 (The Maybes)
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Bayonetta (She was the ballot winner, and Nintendo more or less rescued the IP. It's hard to imagine they'd have a difficult time getting the rights to use her once more. The Switch ports of Bayo 1 and 2 were a good sign, though I'm not sure if Bayo 3 was planned far enough in advance for it to have been put into consideration while finalizing the Smash 5 roster. All that aside, I see third parties as being at risk by nature. And in all honesty, when lining up the third party characters, Bayo sticks out like a sore thumb. She is nowhere near the icon the rest of them are.)
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Sonic (Safest of the third parties, but I think the nature of third party characters provides a room for concern, even if it does seem unfounded.)
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Shulk (I think Xenoblade will get the same treatment as Fire Emblem and Earthbound, and keep the characters from older installments while adding the newest protagonist, but at the same time, I don't think I'd be all that surprised if they did what they intended to do with Ness in Melee and just completely replaced the Xenoblade 1 content with Xenoblade 2).
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Jigglypuff (She was explicitly stated by Sakurai to have been on the brink of being cut in both Melee and Brawl)
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Corrin (I think people underestimate his chance of returning, and find it bizarre that he's considered by so many people to be at a greater risk of being cut than Roy. I wouldn't be surprised if Corrin got cut, but he's still the latest FE protagonist and has a very unique moveset.)
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Robin (If a 100% unique FE rep is going to get axed, it'll come down to him and Corrin. As unique as Corrin is, Robin's even moreso, and represents some important aspects of FE that no other rep in Smash does. Corrin has the advantage of recency, however.)
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Tier 4 (Probably safe, but....)
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Lucario, Charizard, or Greninja (All are extremely popular, but there is a history of Pokemon characters getting cut; Pokemon is the only series that has had multiple cuts in both Brawl and SSB4. If any of them are to go, though, I only see it being one of them; none if Jiggly gets the axe. At the same time, I also would not be surprised if they all made it back in.)
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Falco (I don't see him getting cut, but with the poor critical and commercial reception Star Fox Zero received, I could see them downsizing Star Fox's representation even further this time around. He'd be a surprising cut, but not quite as surprising as any of the characters not listed here)
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Toon Link (This one is only under a very specific circumstance: namely, if the theories some people have about Breath of the Wild Link being a newcomer rather than just a new design for the regular Link. If BOTW Link ends up just being the new version of regular Link, I think Toon Link is completely safe.)
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Mii Fighters (They were a big part of Smash 4, but with the Switch seemingly putting much less of a spotlight on Miis, to the point where they're completely optional and seem to exist only as an extra choice for an avatar, I can see them getting the axe. They'd be much higher on the list if it weren't for how major their addition was made out to be.)
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