This topic interests me, so let's take a look at who's likely to get the axe.
If we eliminate the possibility of veteran characters being cut from the game (as defined by being in two games or more of the series) as well as the early confirmed roster, we come up with this list:
Wario
Diddy Kong
Toon Link
Zerosuit
Metaknight
King Dedede
Olimar
Wolf
Pokemon Trainer
Lucario
Lucas
Ike
R.O.B.
Snake
Sonic
Going down the list, I would say Wario is likely in. He was one of the main featured attractions in one of the opening trailers for Brawl, he has his own franchise series separate from Mario, and is a unique fleshed out character in his own right. Diddy Kong is in for sure, as Donkey Kong is one of Nintendo's big franchises, and Diddy Kong has been the side mascot alongside DK practically from day 1. Like Wario, he's a fleshed out character, and unlike the Mario family, he's not taking up that much more real estate. Metaknight, while problematic in his own right within the competitive Brawl universe, is a personal creation of Sakurai. While he might see a reimagining of his playstyle and moveset, he's far too popular and has too much immunity given he's one of Sakurai's children to get the axe. Dedede being the Bowser of Kirby and sharing the same credentials is no exception either. And finally while Sakurai has expressed the difficulties of dealing with third party ties for the sake of implementing foreign characters, Sonic's popularity and Segas strong and initimate ties to Nintendo solidify his spot in my mind.
Given this, we have this list.
Toon Link
Zerosuit
Olimar
Wolf
Pokemon Trainer
Lucario
Lucas
Ike
R.O.B.
Snake
Toon like I'm 99% sure is getting the axe. The Smash series has had criticism for clone characters since Melee's reveal of its full roster, and Young Link was cut from Melee in favor of Toon Link. On top of this, given that Toon Link is featured as a conductor on a train in one of the new featured stages in one of the trailers, and I think its safe to say he's gone.
Zerosuit Samus I think is more likely to make it in than not. I feel as though her inception was an attempt to expand the character roster while bringing more exposure to the Metroid universe. I also think that if they were to potentially make the transition from Samus to ZSS not require a Smash Ball, it would make her more accessible in the same way Zelda and Sheik are while making way for more characters. Though I don't think that's likely. All in all she was failry unique (albeit poorly designed gameplay wise), but I still feel her leaving the scene is a possibility if they are really hard pressed to find space because from a perspective of personification and not gameplay, ZSS and Samus are the same character, and the audience (casual or not) will see it like that too.
Olimar is only on this list due to popularity concerns. He has the right stuff to be brought back. He has a unique moveset and character design, he has his own franchise with multiple titles, and while he might not be one of the main Nintendo blockbusters, Sakurai isn't one for not using very niche character choices. *CoughG&WCough* This being said however, I feel he is likely to be the most unpopular character given his resume and candidacy. Prior to Brawls roster reveal, I don't think anyone would have predicted that he would have been a playable character to start with. I also think that Olimar's inclusion in Brawl was to try and expose Pikmin more to consumers than it was about bringing a classy new character in, but that's merely my speculation. I'm not fully convinced he's gone, but I think its possible.
I have Wolf on here partly because I don't think he was represented very well in Brawl, and overall was not a very interesting character inclusion. Looking at it from different angles, Wolf was disappointing. From a competitive players perspective, there were expectations of 'the third spacey', a new mechanical toy to play with and master. To say this fell short of what the competitive players may have been looking for is a large understatement, though this can't be entirely blamed on Wolf as a character since Brawl's engine and game design was abysmal. On a casual note, we got 'another character that shoots lasers with a reflector and roughly the same Up B.' While its true that they had different tool kits, what made Fox and Falco interesting in Melee even though they were aesthetically the same outside of texture was that their interactions with everything else while they played were vastly different while still feeling good. Wolfs gameplay did not feel crisp and properly fleshed out in to the same standards as the original two Star Fox characters, even if he had a more feral approach. I feel like a lot of this may just be bias on my end, but I think there was a niche Sakurai was trying to fill here and he just didn't quite do the job right. I also think that with the possibility of Crystal, though unlikely, Wolf could be replaceable. Either way, his inclusion in SB4 is still very real.
Pokemon Trainer's inclusion in Brawl looked like it was supposed to fit some very specific goals in mind. Ones that I think of are adding forms of nostalgia to the player, as well as finding ways of expanding the character roster artificially while still adhering to an arbitrary roster cap. Sakurai stated previously that there are problems with adding too many characters, and I think he knew this going in to Brawl's development quite well, which Pokemon Trainer was one of the ways to help cope with such an issue. I think with this in mind, it might be time to just address the problem directly, in which Pokemon Trainer will be sent packing. I'm going off on memory, but I also believe Brawl was released around the time Fire Red and Leaf Green were big too, so this may have been an attempt to increase game exposure and advertise the same way Olimar for Pikmin was, more so than being included as a legitimate long lasting character. There is also the fact that both Melee and Brawl have had a third 'seasonal' Pokemon included in the form of Mewtwo and Lucario, both of which were very unique and satisfying to play in their own right. With the talk of possibly bringing Mewtwo back (in his new form from X & Y I'd speculate), I also think this makes it quite cramped for Pokemon Trainer among the available seats for the Pokemon slots. Also, if Sakurai is beginning to care about individual character balance issues AT ALL (which I genuinely think he is), I think this would be a big hurdle.
Lucario is on this list soley because he was Mewtwo's 'seasonal' replacement. If the trend continues, we'll see a new one come in to replace Lucario. Also, there's talk of Mewtwo possibly being in from Sakurai. What this tells me is if Mewtwo is possibly on the table, then Lucario has already been sent back to his Pokeball. While he IS a unique character, and the Mario group kind of implies that popularity equals number of seats in the Smash house, I don't see him returning.
Ness and his franchise were much more niche than some of the other big title games being represented here, and I think it was actually quite surprising that a second Mother character made it in to Brawl. Though I attribute this more to Sakurai and Co. submitting to the demands of a larger roster from Melee to Brawl rather than Lucas deserving a spot. I also think its hard to represent Mother characters because all of them have very plain aesthetic appeals, which means including more than one begins to look displeasing. And although I don't follow the games myself, its my understanding that neither character has followed their traditional attacks or moves from the games they originated from. Lucas could have easily just been a skin swap for Lucas, and outside of his inclusion in Brawl, he was not very interesting or popular.
Ike was a good character. He solved the problem Roy had from Melee, and established his own gameplay individuality from Marth. He was a popular character. He felt GOOD to play. Swinging that sword around and clubbing people to death? Hell yeah. And although Sakurai likes to treat Fire Emblem characters outside of Marth as seasonal replacements ala Mewtwo and Lucario, I would much rather see him stay. That said, its for the very reason that Roy was replaced with Ike that I feel his odds are chancy. I FEEL like he has a strong chance to still make it in, though that me be being hopeful and optimistic. Still, he has a chance to get cut.
I actually don't think R.O.B. will be cut. Like Game & Watch, he's made a home for himself in the Smash Bros universe exclusively, and he was a really great character to play. I would almost say he's one of Sakurai and Co.'s children much in the same way Kirby and friends are, as without Smash, most of us wouldn't even know what these two characters were. However, between Game & Watch and R.O.B., the former has been around longer, and if space is really tight for cuts and Sakurai brings his traiditional 'oddball' character in to SB4, R.O.B. might be opted out. While some people might suggest that Wii Fit Trainer and The Villager kind of represent those oddball roster choices (and I agree its possible), both of those are relatively new. Sakurai has a tendency to choose very prehistoric choices. Another thing to think about is that R.O.B.'s story was tied to Subspace Emissary, which is being completely ditched in the new title. I think his chances are strong, but we'll see how it plays out.
Snake, simply put, does not feel like a Smash Bros character. His realism and tone are just a little too much, and it was one of the many things about Brawl from Melee that felt just 'not quite right.' One look at his moveset and you can tell it was littered with confusion as to how to incorporate a character that assassinates and kills people in to a rated E for everyone environment. Sakurai went jumped through a lot of hoops to get Snake in. Not just gameplay wise either, but I'd also assume from a third party perspective as well. Between third party candidates being limited going forward, Sonic and Megaman being SUPER popular to the point of being included almost exclusively on popularity alone, gameplay and design problems, inappropriate context for the characters inclusion in the environment, and just feeling weird, I don't foresee Snake being in the next instalment. I'm not complaining either.