Note: If you really don't want to be spoiled on the Super Smash Bros. roster, then you might not want to continue. This piece contains some information that might be considered spoilers.
My partner and I started played a lot of Super Smash Bros. Melee together in college. I usually took some combination of Link, Marth, or Fox, and she always, always played as the Ice Climbers.
The Ice Climbers appealed to her because she could press forward on the right stick and they would smack the hell out of everything in their way. She got annoyingly good at that, actually, often catching me from behind while I was otherwise engaged. Either that, or she would camp on ledges and shoot ice projectiles. What she lacked in raw skill she made up for in being devious, and as time went on, she became quite versed in their skillset.
Alas, the Ice Climbers are now a confirmed cut from the Smash Bros. roster, meaning that she'll have to stick with King DeDeDe, whom she adopted in Smash Bros. Brawl (she really likes those hammer characters). They join Wolf, Lucas, Pokemon Trainer, and Snake, as well as Melee's Mewtwo, Pichu, Roy, and Young Link on the Smash Bros. equivalent of the Island of Misfit Toys. There was some fear that Ness would be cut as well, but he's back along with (weirdly enough) Dr. Mario and ROB. Fricking ROB.
Most of the cuts are not that surprising. Lucas and Wolf were, to a certain degree, clones of existing characters, with Wolf feeling particularly redundant. Fox and Falco have been kicking around together since Melee, so it felt weird to get Wolf as well, whose main claim to fame was being heavier and hitting harder than his counterparts. The only thing stranger than including Wolf was the decision to make Ganondorf a clone of Captain Falcon.
Anyway, Snake is a more interesting case than Lucas or Wolf. He was a surprise addition to the Smash Bros. roster, appearing partly because Metal Gear Solid creator Hideo Kojima "practically begged" for him to be included. In gameplay terms, he was one of the hardest characters to pick up, but also quite strong if his mines and projectiles were used properly. I rarely used him myself, but I enjoyed codec calls like these:
Snake was one of two third-party additions to the Smash Bros. Brawl roster, igniting intense speculation that Mega Man would also be included (which he was... eventually). But though Kojima seemed amenable to a return engagement, Snake was considered a likely roster cut, and he is indeed gone.
Pokemon Trainer, for his part, was always a bit of a strange one. I used him a lot, but that was more out of loyalty to Pokemon than anything else. Charizard, Ivysaur, and Squirtle weren't the easiest characters in the world to use, and their gradual decrease in damage meant having to switch between them a lot. Playing as Pokemon Trainer meant losing a lot, but as I've long since given up any aspirations of being a tournament player, that didn't bother me too much.
As something of a gimmick character that didn't really work that well, it was reasonable to expect that Pokemon Trainer would get cut. But the Smash Bros. team has instead opted to pare him down to his most popular component, which is evidently Charizard—now a standalone character. I guess I'm in the minority on the front, but I've always preferred Ivysaur to Charizard owing to its long reach, solid projectiles, and powerful upward smash attack. But I'm glad Charizard made the cut, because I still consider its heavy playstyle more interesting than that of Pikachu, Lucario, or any other Pokemon outside of possibly Greninja.
As for the Ice Climbers, I'm still not entirely certain why they were cut. I can't believe it's because they weren't that popular because I've seen them used in venues like EVO. They aren't clones either. They're the only characters out of the ones to cut to have appeared in more than one game, having made their debut in Super Smash Bros. Melee. So what gives?*
*Reader JakeSpencer pointed out this reply from Sakurai. In a nutshell, it's due to hardware limitations. Also, the Ice Climbers aren't a priority as they are unlikely to see another installment in their franchise. That's marketing for you.
My best guess is that the Ice Climbers themselves are rather obscure characters in Nintendo lore, and are unlikely to be recognized by younger players. If that's the case, then it's too bad. I've always viewed Super Smash Bros. as both a tribute to video game history as well as something of an educational tool. As I discussed in my recent breakdown of Mega Man, the game's attention to detail is incredible. As an NES launch title, the original Ice Climber is an indelible part of Nintendo's history, hearkening back to an era when Mario was an upstart and console games were still trying to make a comeback. In that regard, cutting Popo and Nana hurts Super Smash Bros. more than creator Masahiro Sakurai might realize.
I'll admit that even without the Ice Climbers this is probably the most impressive Smash Bros. roster to date. From Mega Man to Fire Emblem's Robin, Sora Ltd. and Bandai Namco have outdone themselves. But I know at least one fan who will be sorely disappointed when she gets a good look at the final roster. I'm sure she won't be the only one.