Weather god
A weather god, also frequently known as a storm god, is a deity in mythology associated with weather phenomena such as thunder, lightning, rain, wind, storms, tornados, and hurricanes. Should they only be in charge of one feature of a storm, they will be called after that attribute, such as a rain god or a lightning/thunder god. This singular attribute might then be emphasized more than the generic, all-encompassing term "storm god", though with thunder/lightning gods, the two terms seem interchangeable. They feature commonly in polytheistic religions. 

Storm gods are most often conceived of as wielding thunder and/or lightning (some lightning gods' names actually mean "thunder", but since you cannot have thunder without lightning, they presumably wielded both). The ancients didn't seem to differentiate between the two, which is presumably why both the words "lightning bolt" and "thunderbolt" exist despite being synonyms. Storm gods are typically male (especially the lightning/thunder ones), powerful and irascible (the irascibility is probably a trait because of the command over thunder/lightning, thus the god's power over this aspect of the natural world influences his personality). Rain and wind deities tend to not be portrayed as wrathful as thunder/lightning deities.

Africa

Ancient Egypt
 Horus, the Egyptian beneficial storm, sun, and war god. Personified in the pharaoh.
 Set, the Egyptian storm god, lord of the desert.

Sub-Saharan Africa
 Umvelinqangi, god of thunder, Zulu mythology
 Mbaba Mwana Waresa, goddess of rain, Zulu mythology
 Oya, the Yoruba orisha of winds, tempests, and cyclones

Americas
 Chaac, Maya rain god. Aztec equivalent is Tlaloc.
 Coatrisquie, Taíno rain goddess, servant of Guabancex, and sidekick of thunder god Guatauva.
 Cocijo, Zapotec god of lightning.
 Ehecatl, Aztec god of wind.
 Guabancex, top Taíno storm goddess; the Lady of the Winds who also dishes out earthquakes and other natural disasters.
 Guatauva, Taíno god of thunder and lightning who is also responsible for rallying the other storm gods.
 Huracán, K'iche Maya god of wind, storms, and fire.
 Juracán, Taíno zemi or deity of chaos and disorder believed to control the weather, particularly hurricanes
 K'awiil, classic Maya god of lightning.
 Q'uq'umatz, K'iche Maya god of wind and rain, also known as Kukulkan, Aztec equivalent is Quetzalcoatl
 Tezcatlipoca, Aztec god of hurricanes and night winds.
 Tlaloc, Aztec rain and earthquake god. Mayan equivalent is Chaac.
 Tohil, K'iche Maya god of rain, sun, and fire.
 Tupã, the Guaraní god of thunder and light. Creator of the universe.
 Yopaat, a Classic-period Maya storm god.

Asia and Oceania
 Adad, the Assyrian storm god
 Ba'al, Canaanite god of fertility, weather, and war.
 Hadad, the Canaanite and Carthaginian storm, fertility, & war god. Identified as Baʿal's true name at Ugarit.
 Fūjin, Japanese wind god.
 Indra, Hindu thunder/lightning god. 
 Küdryrchö Jumo, the Mari storm god.
 Marduk, Babylonian god of water, vegetation, judgment, and magic.
 Mariamman, Hindu rain goddess.
 Raijin, Japanese god of thunder, lightning, and storms
 Susanoo, tempestuous Japanese god of storms and the sea.
 Tamar (goddess), Georgian virgin goddess who controlled the weather.
 Tarḫunna, Hittite storm god; other Anatolian languages had similar names for their storm gods, such as Luwian below.
 Tarḫunz, Luwian storm god.
 Tāwhirimātea, Maori storm god.
 Teshub, Hurrian storm god.
 Theispas or Teisheba, the Urartian storm and war god.
 Vayu, Hindu/Vedic wind god.
 Vayu-Vata, Iranian duo of gods, the first is the god of wind, much like the Hindu Vayu.
 Weather god of Nerik, Hittite god of the weather worshiped in the village of Nerik.
 Weather god of Zippalanda, Hittite god of the weather worshiped in the village of Zippalanda.
 Yahweh, Hebrew divine warrior and god of the entire cosmos.
 There was no single storm god in Chinese mythology. There had to be many deities for a single storm:
 Dian Wu, Leigong, and Wen Zhong, the Thunder Deities.
 Feng Bo, Feng Po Po, and Han Zixian, the Deities of Wind.
 Yunzhongzi, the Master of Clouds.
 Yu Shi, the God of Rain.
 Sometimes the Dragon Kings were included instead of Yu Shi

Europe
 Aeolus (son of Hippotes), keeper of the winds in the Odyssey
 Anemoi, collective name for the gods of the winds in Greek mythology, their number varies from 4 to more
 Audra, Lithuanian god of storms
 Bangpūtys, Lithuanian god of storms and the sea
 Freyr, Norse god of rain and sunshine
 Jupiter, the Roman thunder/lightning and sky god and king of the gods
 Perkūnas, Baltic god of thunder, rain, mountains, and oak trees. Servant of the creator god Dievas.
 Perun, Slavic god of thunder and lightning and king of the gods
 Tempestas, Roman goddess of storms or sudden weather. Commonly referred to in the plural, Tempestates.
 Thor, Norse god of thunder/lightning, oak trees, protection, strength, and hallowing. Also Thunor and Donar, the Anglo-Saxon and Continental Germanic versions, respectively, of him. All descend from Common Germanic *Thunraz, the reflex of the PIE thunder god for this language branch of the Indo-Europeans.
 Taranis, Celtic god of thunder, often depicted with a wheel as well as a thunderbolt
 Ukko, Finnish thunder and harvest god and king of the gods
 Zeus, Greek thunder/lightning and sky god and king of the gods