Gonna try to get them all out at once...
Parents: Lucario + Luxray
Shared egg group: Field
Offspring name: Luxrio
New type: Fighting/Electric
New base stats: 85/125/84/115/84/90 (Standard) (BST: 583)
85/160/102/140/84/112 (Lucarionite) (BST: 683)
New ability and desc: Inner Focus + Intimidate = Battle Stance: Lowers opponent's Attack one stage upon switching in. Cannot be flinched by intimidated opponents. Gains Adaptability upon mega evolving.
Notable moves: Swords Dance, Nasty Plot, Close Combat, High Jump Kick, Superpower, Thunderbolt, Focus Blast, Charge Beam, Aura Sphere, Wild Charge, Power-Up Punch, Vacuum Wave, Extreme Speed, Ice Punch, Dark Pulse, Flash Cannon, Bullet Punch
Role identification: Wallbreaker with the ability to go Physical, Special or mixed. Fighting/Electric is a pretty sweet STAB combo, and Mega Luxrio backs it up with massive 160/140 offensive stats and a great ability in Adaptability. It also has all the coverage options it could possibly want regardless of what direction it goes in, so go nuts with that. On top of that, its base form's ability gives it more opportunities to set up safely, though its defenses are pretty average regardless, so be careful about switching it in.
Parents: Sylveon + Miltank
Shared egg group: Field
Offspring name: Syltank
New type: Normal/Fairy
New base stats: 105/82/95/85/110/90 (BST: 567)
New ability and desc: Cute Charm + Thick Fat = BBW: Contact with user has a 30% chance of causing infatuation. Resists Fire and Ice- type moves.
Notable moves: Stealth Rock, Reflect, Light Screen, Wish, Heal Bell, Milk Drink, Seismic Toss, Counter, Thunder Wave, Toxic, Yawn, Safeguard, Moonblast, Hyper Voice
Role identification: Bulky support. What it lacks in offensive power, it more than makes up for with its 105/95/110 defenses, its wide variety of support options, its decent defensive typing, and its unique ability which makes it rather difficult for offensive mons (particularly physical ones) to pressure it. Seismic Toss and Counter are both viable options if you don't want to invest in Attack or Special Attack at all.
Parents: Pidgeot + Noivern
Shared egg group: Flying
Offspring name: Pidgevern
New type: Normal/Flying
New base stats: 94/85/87/93/85/122 (Standard) (BST: 566)
94/85/92/158/95/142 (Pidgeotite) (BST: 666)
New ability and desc: Tangled Feet + Infiltrator = Bumbling Spy: Gains the ability to bypass substitutes and screens if afflicted with any status, including confusion. Gains No Guard upon mega evolving.
Notable moves: Hurricane, Boomburst, Focus Blast, Heat Wave, Draco Meteor, Roost, Tailwind, U-turn
Role identification: Basically Mega Pidgeot on steroids. It finally gets the coverage option it always wanted in Focus Blast, as well as absurdly powerful STAB coverage on both sides (Hurricane + Boomburst), and Draco Meteor without that annoying 10% miss chance. Decent bulk for an all out attacker, too.
Parents: Tyranitar + Aurorus
Shared egg group: Monster
Offspring name: Tyranaurus
New type: Rock
New base stats: 121/115/101/107/106/69 (Standard) (BST: 619)
121/145/141/107/126/79 (Tyranitarite) (BST: 719)
New ability and desc: Sand Stream + Refrigerate = Granulate: Normal- type moves become Rock-type moves and gain a 30% boost in power.
Gains Sand Stream upon mega evolving.
Notable moves: Return, Hyper Voice, Stone Edge, Dragon Dance, Calm Mind, Stealth Rock, Dragon Tail, Superpower, Crunch, Pursuit, Focus Blast, Fire Blast, Ice Beam, Thunderbolt, Rock Polish, Thunder Wave, Roar, Dragon Tail, Haze, Reflect, Light Screen, Rest, Encore
Role identification: What's interesting about this fusion is that its base form seems to be just as viable as its mega form; if not more, in some respects. I imagine that base Tyranaurus would work better as an offensive sweeper, which seems odd considering its inferior offensive stats, but keep in mind that base Tyranaurus has both a) the ability to hold an item to boost its power, and b) an ability that gives it much stronger STAB options (base Tyranaurus's Return hits harder than Mega Tyranaurus's Stone Edge, to put things in perspective).
On the other hand, its Mega form could work surprisingly well as a supporter/ hazard setter. It has much better bulk, and it enjoys the SDef boost it gets from Sand Stream. It also has a surprisingly wide array of support options, including Thunder Wave, Haze, dual screens, Dragon Tail and Roar. Its lack of reliable recovery still hurts it, but a RestTalk set could work in theory.