bugmaniacbob has an excellent post.
Read it.
Yanmega-
The biggest glaring issue is Stealth Rock, of course. Its mostly a concern of what we're dealing with. Such a huge SR weak and Yanmega's obvious defense issues because of it means if you're using it in an offensive core style. A Partner with Rapid Spin would work, but any Spinner also helps other Pokemon with SR weaknesses, notably Zapdos, Salamence, and Gyarados. It also weakens offensive options generally because one slot will be going to Rapid Spin, potentially reducing offensive coverage by that much more. Combined with Yanmega's weakness to all 3 "big elementals" (Fire, Electric, Ice) and it's a tough road to hoe.
Froslass-
Unlike Yanmega, a 2x Stealth Rock weak isn't the kind of a gamebreaker a 4x weak is. Froslass also has a few immunities to its name, and employs a solid Spiking strategy. It's still not an ideal typing defensively, but it does enough and its worst weaknesses are Fire and Steel, both of which are resisted by Water and Fire.
Raikou-
Raikou is pretty solid on it's own, with no really glaring weaknesses. The difficulty will be breaking new Ground because there are loads of offensive pokemon immune to Ground, but none have really managed to bring Raikou into the limelight.
Zapdos-
Zapdos already has a sort of defensive core with Breloom, spreading status and blocking the opponent's momentum. Otheriwse Zapdos is fairly well-contained, and bringing a Pokemon to help out specifically it will be more difficult.
Togekiss-
Togekiss has a lot of potential if only for its sheer diversity of sets. It can already provide a Plotpass boost for a sweep and has existent, if limited resistances/immunities. The only real question is deciding which set to focus on, since Togekiss has offensive and defensive capabilities.
Heracross-
Life used to be Hera weak, and now it isn't. I don't necessarily believe something that benefits Heracross inherently benefits Lucario, since Heracross has important Fighting and Ground resistances that Lucario is susceptible to, generally better defenses, and more raw offense.
Staraptor-
Colossoil seems to have done a bang-up job bringing Staraptor into the limelight, even if that wasn't part of the original purpose. I'm mostly afraid that we'll cover similar ground to Colossoil because of the kind of walls Staraptor tuns into.
Umbreon-
Scizor is probably it's biggest issue, since the Bug weakness combined with Scizor switching out after U-turn is the biggest nuisance. Weakness to powerful fighting attacks with no decent answer (Psychic?) is also an issue. Regardless, Umbreon can also pass boosts and aside from these sticking points, has a great deal of potential in a defensive core.
Weavile-
I simply don't see the interest in Weavile. Defensively speaking there is nothing capable of fending off the combined weaknesses of Ice and Dark, as the two types have no internal synergy whatsoever. This leaves Weavile in the "breaker" role of an offensive combination, a rule it is poorly suited to. It's strongest STAB attack is Ice Punch at Base 75, with Night Slash coming in at Base 70. Weavile does not even possess Superpower despite it generally being dished out to Pokemon with 110+ Base Attack, needing to rely on Brick Break and Low Kick.
Weavile does have fairly good technical prowess between Ice Shard and Pursuit, but that's the extent of its abilities. The only spinner it forces to think twice is Starmie. Starmie is the most popular, but it's not the only Spinner. It needs Night Slash for Tentacruel, since Tentacruel resists all else and will just set up Toxic Spikes after Spinning. Donphan has left OU and Weavile really needs Ice Punch to deal with it. So it's really locked in a corner between displaying its good technical qualities and addressing Spinners. It can't do either of those and still have the coverage to be the breaking portion of an offensive core.
Ultimately I don't think Weavile will produce anything near "good discussions." There will merely be endless fighting over which of its weaknesses (SR, Bullet Punch, Fire moves, Fighting moves, U-turn) its partner should address. It's certainly possible to try and address them all at once, but it puts you in a typing and ability straight jacket with an entirely incoherent result. In the end it will overshadow Weavile rather than being its partners, and less limited partners will take its place.
Honchkrow-
Honchkrow has a much more accommodating typing combination, as well as an excellent mixed movepool and support moves and the stats to back up either. SR weakness is a liability but can be worked around, especially with Honchkrow's Pursuit resistance and Roost. Honchkrow definitely has the skills to be the breaking portion of a combo and can even lend support.
Porygon-Z:
Porygon-Z has some of the scariest offensive potential out there. It's got a ton of initial power and a boosting move in Nasty Plot, as well as Agility and Adaptability to help out Normal's lack of SE hits. It also only has one weakness to cover, which is very helpful. It's major weak point is susceptibility to status, with Paralysis being the most crippling. I think Porygon-Z has a lot of potential based on it's pure power. A good partner might be one that can absorb status and utilize Safeguard, then perhaps U-turn or Baton Pass to Z to let it finish the job. Bug might have SR weak but it would have STAB U-turn and resists Fighting. It'd be an interesting direction to go in.
Shaymin-
Shaymin has a good core movepool and solid defensive abilites, as well as Natural Rest allowing it to switch out effectively. Pure Grass has its weaknesses but is also fairly easy to work with. What I'm most afraid of is that we already have so many Water CAP Pokemon and Fire and Ice are the most pressing weaknesses. Otherwise there is a great wealth of sets that could be used with Shaymin.
Celebi-
Celetran is already infamous as a combo. I'm not too keen on building a CAP for a mon that's already part of an established core, which Celebi most certainly is. I think we'd learn much more from the similar Shaymin.
Abomasnow-
Much like Weavile, Abomasnow leaves much to be desired defensively, although at least Abomasnow has relevant resistances to Earthquake and Thunderbolt. The hardest part about Abomasnow is that it's a poor team player with non-Ice types because of Snow Warning, making it difficult to build a core around it.
Gallade-
Gallade is interesting because it has possibly the largest support movepool of any of the nominations. It also has a fairly unique typing and an excellent array of attack types, with the power to back it up and Swords Dance.
Building a partner around Gallade would still be difficult because physical Psychic attacks are a distinctive quality of Gallade, but so few Pokemon use them in standard, and it took multiple Psychic-weak Pokemon to bring about their use in full CAP. Nonetheless Gallade has a lot of material to work with.
Ninjask-
Ninjask is a pretty good team player already, but suffers from being easily phazed out. A two-Pokemon combo that could benefit immediately and take out most of the Phazers would do quite a bit for Ninjask, my only worry is that it would be a little too straightforward since it screams "physical attacker with Suction Cups" at the outset.