1. Power Ups (Mario Characters)
The Super Mario characters have a wealth of possible alternate costumes at their disposal, none more evident than the power ups. We got the beginnings of this in Brawl (Fire Mario, Fire Luigi), but with Peach, Rosalina and Bowser also on the roster, so much more can be done. The first thing to do is give Peach and Rosalina matching "fire" alternate costumes. Give Bowser a costume based on Meowser from Super Mario 3D World; costumes based on the hammer/boomerang suits, ice flower, and copter suit are also all possible and just a fraction of what could be utilized here.
2. Alter Egos & Other Things (Mario Characters)
Another for the Super Mario franchise, as well as Donkey Kong. While it would mean no Funky Kong character, a costume based on him could work for DK. For Bowser, you have many options - Dry Bowser, Dark Bowser, Dreamy Bowser, Bowletta, the blue ox from Super Mario Bros., or Wedding Bowser? On that note, I'd like to see both Mario and Luigi receive alternate costumes depicting them as Dr. Mario and Dr. Luigi respectively - Luigi could also use a costume based on Mr. L. Peach could receive a costume based on her appearance as the Shadow Queen in Paper Mario: The Thousand-Year Door.
3. Yarned Up? (Kirby, Yoshi)
While I can't help but think it'd be cooler to have Yarn Kirby or Prince Fluff as a full-blown character (preferably the latter), if it isn't happening I'd like to see some of our fighters going yarn in alternate costumes. Yoshi, Kirby, Metaknight and King Dedede have already been seen in yarn format, so maybe it could happen.
4. Misc. Outfits
Why not have costumes for both Link and Toon Link in their various pre-adventure outfits? Wind Waker, Twilight Princess and Skyward Sword come to mind immediately, although this one might be less possible due to the appearance of train-garbed Link from Spirit Tracks in a stage already. The same could be said for Zelda, as well as Ness and Lucas in various outfits. Fox, Falco and Wolf could all have outfits from previous games in their franchise available as costumes. For characters like Samus, where the different suits offer minor variations on the aesthetics of the armor, those minor modifications could be added instead of making them a simple recolor.
5. Shiny Forms (Pokemon)
Of course, this entry would be lacking if I did not discuss Pokemon. Honestly, I'm not sure why this hasn't been implemented at all yet - why are we being given Pokemon who wear hats instead of, y'know, actual recolors? Shiny forms are a must, but the colors for Charizard in Project M (which is a whole other entry unto itself) prove that you can get very creative with every color costume for Pokemon. If Mega Evolution forms are not implemented as the aftereffects of a final smash, this is also the perfect place for them to come into play (assuming that the mega evolution is not how that particular Pokemon is represented). And, as the image of Mewtwo above shows, there are many other options for Pokemon as well.
Several images in this entry (Mewtwo, Mr. L, Toon Link) are from Project M, a fan created moderator for Brawl. I suggest you check it out if you prefer Melee to Brawl, want something new to tide you over until the new game comes out, or if you're just curious. I'll be discussing Project M and what it could mean for the future of the series in another file at a later date - for now, feel free to argue in the comments with me regarding my opinions on alternate costumes.