Man, this is gonna affect a lot of things:
Grass types- Now with Shaymin gone, Grass types that were previously eclipsed by Shaymin are now going to be much more common, especially to check Rhyperior now that Milotic is gone too. Tangrowth, Sceptile, Rotom-C, Gourgeist, and Virizion are some things that come to mind. Tangrowth has similar offensive stats and bulk to Shaymin, but is much slower. Its probably going to be replaced on more bulky offensive teams utilizing Shaymin. I foresee Virizion a very dangerous threat. With its Fighting typing, it can set up on a variety of threats, including but not limited to Rhyperior. Plus, now that Raikou is gone, base 108 speed is quite fantastic. Rotom-C can play both a defensive role with Will-O-Wisp, or go on the offensive with a Choice Scarf. Sceptile is still an offensive powerhouse, and can easily be a great late game cleaner once things like scarfed Braviary are gone.
Tornadus - I mean, do I need to say more? There's a pretty solid chance its going to get banned, so I'm just not gonna waste time talking about it. A shame too, since I really enjoyed using it. Btw, specially defensive Rotom-S (which is what people really should be using) is a great counter; it takes LO Hurricanes like its nothing, can burn physical variants, and OHKO it back after SR. Plus, Rotom-S is still a great pokemon, and checks a big portion of the meta, and is really underrated in my opinion. Still, Tornadus is probably going to get banned anyway. :/
252 SpA Life Orb Tornadus Hurricane vs. 252 HP / 252+ SpD Rotom-S: 78-92 (25.6 - 30.2%) -- 0.7% chance to 4HKO after Leftovers recovery
Water-types: Now with Milotic gone, Slowking, Jellicent, and Lanturn are probably going to rise. The three are probably the only things that could replace Milotic's role as a wall. Also with Raikou gone, water types are quite a bit more viable, except Lanturn, who benefited from Raikou's presence.
Defog: With Milotic gone, and probably Tornadus soon afterwards, there is little to punish Defog users. Milotic was pretty much the only viable Competitive user, and so the only thing Defoggers have to worry about now is Braviary. With this being said, Gligar and other defoggers are probably going to rise in usage.
Rhyperior - Now, I'm a little bit mixed about this one. Rhyperior absolutely hated Shaymin, so you'd expect it to rise in usage. However, with dangerous new Grass-Types running around, like Substitute Sceptile and Swords Dance Virizion, I'm a bit unsure, as it can go either way.
So yeah, there's my two cents, for what its worth.