The idea for them I had was Deoxys' crystal(aka, its brain) being replaced by a common item, either evolutionary stones, pieces of life force of Pokémon, or Elemental Gems, which allows them to get different body styles and forms.
Legendary Heralds and Guards: Various species of Pokémon serving as servants of legendary Pokémon, these species would be granted the unique moves and abilities of their respective legendary. They would serve as common wild encounter or mid-bosses of their legendaries. Competitively, they would be a way of bypassing Uber species' unique moves to common mons.
This idea developed from an older idea I had, where certain species would act as subordinates to their associated legendary and gain stat boosts when they are used alongside them, which would be disconnected to their ability. However, I expended the idea a bit to make it more sense in Pokémon world, and fit in the lore we have, such as Arcanine being showcased alongside Kanto birds.
Giga Forms: Another Mega Evolution-like gimmick, but the difference would be that instead of reaching their potential, these species would get abnormally larger, giving rise to what we know as "Giant Pokémon". These forms would be usable by all stages of Pokémon, but only few would get proper Mega Evolution-esque form changes.
The downside of this would be the increased Low Kick and Grass Knot damage, as well as decreased evasion and speed, though these would only count for certain species, with few others escaping these downsides.
Mature Forms: Attained after refusing evolution for a while, a Mature Form for a Pokémon would be attained for a Pokémon who has refused to evolve for a long time. These variants would keep the same BST as their final evolved forms, but their stat distributions would be different. Once they attain this form, however, they would lose their ability to evolve and use Eviolite permanently. Effectively, they would become like Eternal Flower Floette.
Mature Forms for Baby Pokémon might be able to breed.
Chibi Forms: Same as Giga Forms, but in reverse. These would be tiny, smaller forms of Pokémon, alluding to shorter variants of their species. Only some species would get true Chibi forms, while others would get just small.
The downside of this would be loss of offensive and defensive power, in favor of increased speed and automatic Minimize.
Living Mega Stones/Form Changers: These species would allow a species to reach to their proper Mega by simply being on the team. These species would have some characteristics of their Mega partners. They would serve as vehicles to have regular Mega Evolution without any item, or nasty backstory of "Key Stones are people!"
These species might have different forms and/or stat boosts while the Mega is activated and in the team. Certain abilities would also work as this, but serving an all purpose for all or some Megas.
Brute Force variants: These variants would belong to species that are known to have unique items and clothes. Instead of these, they would go completely wild, gaining new BSTs and abilities.
For example, Farfetch'd without its Stick would get 450 BST and become Water/Flying, but it would be unable to use its Stick.
Aggressive/Calm variants: These would be behavioural variants of the existing species, acting similar to regional variants. They would change how a Pokémon plays and looks and they would alter the moveset, but typing would remain the same. In rare occasions, such as Slaking, they might change BST altogether.
Other ideas proposed:
School Forms: Various other species are known to gather in large groups such as Unown and Combee, these species can also benefit from School Forms. And weak initial and second stages can benefit from such a thing.
Zen Mode: Same as above, several species are known for their latent psychic powers and ability to meditate, so these species can also get Zen Modes.
Interrupted evo: http://icaro382.deviantart.com/gallery/?catpath=%2F&q=interrupted+evo
There are other concepts I have mentioned in the past, but I don't see any point in repeating them here.