Weather-based strategies:
Rain:
Use the power of Rain to give a bonus to Water-attacks, as well as soften Fire-type weaknesses and make Thunder and Hurricane unavoidable. Pokemon generally used in the rain include Toxicroak, Ferrothorn, Jellicent (comboes with Surf), Kingdra (because of Swift Swim), Ludicolo, Volcarona (due to Hurricane), Tornadus, and Thundurus. Politoed is a must due to Drizzle, which triggers the rain.
Sun:
Use the power of Sun to power up Fire-type attacks, softening any Water-type weaknesses and allowing you astronomical damage output. Not a lot of Pokemon do well in Sun, but notable ones include Darmanitan, Volcarona, and Heatran, although there are others. Ninetales is a must due to Drought, which triggers sunlight.
Sandstorm:
Sandstorm is a fierce condition indeed, damaging non-Rock/Ground/Steel types each turn, giving Rock types a 50% boost to Special Defense, and triggering some exceptionally powerful abilities. Tyranitar and/or Hippowdon is used to activate the weather, and Sandstorm usually uses Garchomp and/or Excadrill as an attacker, due to Sand Veil/Sand Rush respectively. Anything that is Rock/Ground/Steel in any combination will feel right at home. Earthquake and Rock Slide are ludicrously common among Sandstorm teams, and Rock Slide is commonly seen even outside it.
Hail:
Hail isn't as often seen, as there are even less Pokemon that can exploit it than Sun. However, it will damage any non-Ice types (which include most if not all common Pokemon), as well as make Blizzard, which will hit BOTH opponents, unable to miss, making this condition absolutely terrifying. It usually comboes with Trick Room as most Pokemon that use Hail are none too fast. Abomasnow is obviously a must for the team, and things like Walrein make for fantastic additions. Generally, the more Pokemon you can get to run Blizzard, the better. In addition to Walrein, Glaceon and Froslass combo well with Hail, but don't rely on them exclusively as Ice-types have a lot of weaknesses. Try pairing them with things that can switch in to Ice's weaknesses.