Okay, I thought answer this one.
Weather initiators: [Sand] Tyranitar , Hippowdon, Hippopotas; [Rain] Kyogre, Politoed; [Sun] Groudon, Vuplix, Ninetales; [Hail] Snover, Abomasnow.
These guys are all the pokemon capable of starting up permanent weather for you. Note that these pokemon are not required to make a weather team, but they make excellent allies. This becomes more apparant in the lower battling areas of pokemon such as NU. I've broken the rest of this up by the type of weather.
Sand (OU)
Excadrill-This pokemon is built completely around sand sweeping. If you've seen a sand team, you've seen Excadrill. I don't even have to explain this guy.
Gliscor -He's got all around bulk, can heal with toxic orb then fling it for plenty of passive damage, and can stop several other pokemon the opponent has that might benefit from the sand.
Garchomp-High attacking stats, sand veil, passive damage, you get the idea.
Heatran-Like most of the other pokemon here, he doesn't take damage from the sand, and his flash fire ability can help force several switches on pokemon, and even more when he carries around a air balloon.
Metagross- His typing leaves him with hardly any weaknesses, and can force more switches, perfect when stealth rock is active.
Aron-see FEAR strategy. Not the most common, but still a potential threat in the sand.
Landorus-Typical sand pokemon. His ability helps him benefit from it, and he shares the same typing as Gliscor.
Forretress-Entry hazards are all He's about.
Ferrothorn-He relies a lot on passive damage, so the sand can do a good job for him. He can also be a great asset on rain teams, since the rain helps cut his fire weakness down a bit.
Sand [UU]
Gastrodon-Gastrodon can be a great way to take water type attacks, which many sand teams are weak to. Thanks to his storm drain, he can safely switch in and hit back with quite a bit of damage. He can be a nice asset on a rain team as well.
Nidoking/Queen-The sand doesn't help them too much, but toxic spikes tends to be a problem for sand teams in UU; thanks to these guys, you are able to absorb the spikes and stop that before it becomes a problem. They are also able to hit back pretty well thanks to sheer force, offering more special attacking for sand teams.
Marcatus/Cacturne-Pretty much the same as gastrodon, just different typing, and they can take grass moves.
Rotom-H-He is a nice way to deal with grass pokemon if you use Gastrodon. He can come in on energy balls, popular on things like Mismagius, and hit back with shadow ball or STAB fire.
Any rock pokemon-This goes for OU or UU. Regirock, Gigalith, Rhydon, and Aggron are popular choices. The special defense boost helps balance out these physical behemoths, and they all have pretty good movepools.
Gligar-He's a lower tier version of gliscor, really.
Sandslash-He's a lower tier version of Excadrill, but with more bulk.
Rain
Gyarados/Feraligatr-Physical sweepers made even stronger
Dragonite-He's got the perfect rain set with Surf (powered by rain), thunder (100%), and hurricane (100% and STAB) He's the only pokemon to get this combo, save for a smeargle, and his mutliscale makes him a hard guy to take down.
Scizor/Skarmory, Bronzong, etc-Steel types. They lose a bit of fire weakness thanks to the rain, making them very difficult to take down.
Raikou-Weather ball, STAB thunder, the works.
Suicune,Jellicent,vaporeon, etc-Water absorb, Water STAB, he's pretty bulky too.
Ludicolo-Rain staller, can get rain dish and leftovers health, and even leech seed.
Kingdra/Kabutops-Anything with Swift swim is of use, but Kingdra is the most popular.
Carracosta/Cloyster-Shell Smash+rain...Nuff said. Cloyster can sub break, while Carracosta has sturdy and aqua jet to help him out.
Hail
Walrein-He's the ultimate in hail stalling thanks to his ability and bulk.
Mamoswine-Ground typing, Ice prioty, and he hits hard. He's on almost every hail team I've seen.
Froslass-Spikes, fighting immunity, self explanatory.
Weavile-He's fast, and he sweeps.
Regice-He's a pretty bulky pokemon, and the hail helps him out.
Anything with snow cloak, ice body, etc. Vanilluxe comes to mind, but Hail relies more on the ability abuse in UU than the other weather forms,and for good reason.
Sun [OU]
Volcarona-Dear god have mercy on us all.
Cryogonal-He might see use to help deal with water types, and can help rapid spin things.
Venusaur-Any chlorophyll pokemon will do, but he's especially popular. His growth and his synthesis can all be an asset.
Espeon-Espeon can help deal with physical pokemon, scare off fighting types, and can use morning sun for recovery,
Infernape-He can go for mixed sweeping and can kill pretty much whatever you want it to kill.
Sun [UU]
Charizard-His solarpower makes him a pretty dangerous pokemon in the sun.
Victini-High powered STAB+sun.
Typhlosion-He's one of the few pokemon to get eruption. That+Sun is devastating.
Arcanine-STAB fire, and he can shrug off damage thanks to morning sun.
Umbreon-bulky power, and moonlight can help him out.
Tangrowth-He's a lower tier Venusaur.
"Immune" pokemon
These pokemon aren't assigned to a specific weather, but have an ability that can help them out.
Mandibuzz,Alakazam,Reuniclus,Clefable,Xatu, etc
Notable anti Weather pokemon
Altaria-A nice check to sun teams. a 4X grass resistance, resistance to fire, and nice bulk. Its ability will force the opponent into going without weather, which is bad if you have someone use solarbeam as bait.
Gastrodon-He gets dangerous very quickly if you are using a rain team. He can absorb water attacks, get thunder immunity, sponge special attacks (which make up a large amount of rain members) and take neutral ice moves well. His storm drain gives him a special attack boost, and unless your pokemon has water immunity of its own, you'll get hit by a STAB+rain boost+Special attack boosted Gastrodon.
Gliscor-He's immune to ground and neutral to rock. He also resists fighting, and is able to deal with sand pokemon pretty well, despite benefitting from the sand himself.
Hariyama-His thick fat and fighting typing help pay off for sun and rain teams.
Stealth rock-Use this against a hail team and watch the magic happen.
There are plenty of others, but those are a few favorites of mine.
