Africa

In September, along the coasts of the Red Sea it's still too hot. Along the coast of Morocco there can still be fog and mist in the morning, and the sea is still cool, but all in all you can go. In the Southern Hemisphere it is late winter, and at tropical latitudes it can still be a little cool. In Mauritius it can be a little cool, and there can be a moderate wind and some rain.
Where to go: Canary Islands, Comoros, Kenya, Madagascar, Madeira, Morocco (Atlantic Ocean), Mayotte, Mozambique, Seychelles, Tanzania, Zanzibar

Asia

The monsoon is still active in much of Southern Asia.
Where to go: Indonesia (Bali, Walea)

North and Central America

In the Gulf of Mexico and Central America the weather is hot, muggy and rainy, and there's the risk of hurricanes. In the coast of Southern California, the sea is still quite cool, but as in August, it goes a bit better than in July.
Where to go: United States (Los Angeles), Mexico (Baja California north)

Caribbean Sea

Like August, September is hot and humid, with abundant rainfall, and a concrete risk of hurricanes. If you are lucky you may well experience a nice period, but generally this is not an advisable month. The driest islands, and the most sheltered from hurricanes, are the Leeward Antilles (Aruba, Bonaire, Curacao), as well as the islands of Venezuela.

Mediterranean Sea

The summer begins to decline in the northern part, while a hot and sunny weather still reigns supreme in the southern part. In the Spanish and Moroccan part of the Alboran Sea, the sunshine lingers on, but the sea is still a bit cool, due to the infiltration of cool waters from the Atlantic.
Where to go: Albania, Algeria, Cyprus, Egypt, Italy (south), Greece, Israel, Lebanon, Malta, Spain (Balearic Islands, south coast), Tunisia, Turkey (west and south coast)

South America

It's the dry season in Guyana.
Where to go: Brazil (Belem, Fortaleza), Guyana (Georgetown), French Guiana, Suriname

Oceania

In the Southern Hemisphere winter is ending, but the situation is more or less the same as in August: it's better to go to the islands which are not located too much to the south.
Where to go: Cook, Fiji, Christmas Island, Cocos Islands, Kiribati, Nauru, Niue, Papua New Guinea (Port Moresby), French Polynesia (Tahiti, Bora Bora, Marquesas Islands), Solomon Islands, Samoa, American Samoa, Tokelau, Tonga (north-central), Tuvalu, Vanuatu (north)