Ver 2.0 Edit: I've clarified a bit more how this list should be read. Check it out if you wish.
First off, I'm going to go ahead and say that I'm not entirely sure there will be a large increase in character amount - but there may be a large amount of new characters. I don't think it's a totally far-fetched idea that quite a handful of Melee characters are replaced, and the sum total ends up being around 26, but with all unique movesets and a good chunk of new faces. This is based partly on Sakurai's comment that last time it was difficult to get up to 26 characters, but this time they will try to do so again. It could mean get such a large increase again, or get a cast of about the same size again - which the latter would really only be difficult if there were major shake-ups in available characters.
That being said, here's the characters I think could get the boot, in order of likeliness; when a section says and/or, it means I think it is likely that at least one of those will be eliminated moreso than one from the group below it. So, even though Sheik is below Marth, it's not that I necessarily think Marth is less likely than Sheik, just that one of the FE characters being eliminated is more likely than Sheik being eliminated. Same with Falco and the Ice Climbers; I think it's more likely that one of the 'Classic' characters be eliminated than it is Falco, not that either one of them has a higher chance than Falco by themselves.:
1. Doctor Mario, Pichu, Young Link - These characters, even though I love Young Link, do not bring much of anything to the table. Not only are their movesets slightly modified versions of their clones, but their characters are as well. Even giving them unique movesets might not salvage these three, as they're just so... unremarkable. Sakurai likes unique characters, and these three are clones in more ways than one. Not to mention that Mario has stolen Doc's fair now, which seems to be a hint.
2. Marth and/or Roy - I'm leaning towards Marth being eliminated here. While it's debatable who is really a clone of who, remember SamuraiPanda's translations of Sakurai's comments; the one where he remarked on the man who was very pleased about Roy being in. While Marth is more popular to play as due to him being a better character, Roy seems to certainly be more 'famous' and liked by the general audience, and maybe, just maybe, even mean a bit more to Sakurai himself. So I'd vote for a revamped Roy and the elimination of Marth rather than vice verca. Of course, it's possible both could be cut and other FE characters are added in accordance with that FE stage.
3. Mr. Game & Watch and/or Ice Climbers - Both of these were very old, very obscure characters that never gained much popularity (IC somewhat in later years, but, eh). Now, Sakurai does like obscure or unique characters, but I think these two may be too obscure. The out-there characters, I believe, are there to make the player go "Oh, that guy? I would've never guessed, cool", whereas with these two most just thought "...Huh?" There's better oddballs to replace them with.
4. Falco - Falco is a relatively good choice from Starfox, but I'd say there's better ones, namely, Wolf and Krystal. If he comes back he should be at least Luigified, but I won't miss him if he doesn't return.
6. Ganondorf, Mewtwo, Sheik, Ness - I think these three are probably going to see a comeback, but who knows. I feel all four have a big enough chance of being eliminated to be considered. Ness is the only original character I can conceivably see being eliminated, but only if he is replaced by Lucas. Ganondorf is the same - only eliminated if he is replaced by another Zelda villain, perhaps even his 'Ganon' form.
12 characters to cut is quite a bit, but after 3 or 4 I say it's pretty unlikely, along with both Mr. Game & Watch and Ice Climbers being eliminated or both Marth and Roy being eliminated. We'll see though. I honestly wouldn't mind shedding off a chunk of less-than-stellar characters for fresh and interesting ones.