By boat: Sea transportation between islands will make you discover the charms of a picturesque cruise between Tahiti and the Leeward Islands (Huahine, Raiatea, Tahaa, Bora-Bora, Maupiti), but also to the Austral, Tuamotu and Marquesas islands, aboard freighters with passengers accomodations or small fishing boats with cabins for eventual passnegers. An amazing experience, not to mention that the cost is definitely cheaper than by plane and that the atmosphere is very authentic (plan on 30 Euros, for exemple, to go to Huahine with 8 to 10 hours at sea after leaving Tahiti). Timeliness and comfort however are not always guaranteed, especially if the ocean is bad. .
Tahiti-Moorea ferries: Transportation between Tahiti and her sister island, Moorea, is provided by several ferries and fast shuttle boats (between 30 and 60 minutes depending on which ferry). Over 10 trips daily. Moderate fare: between 12 and 15 Euros roundtrip
Cruises: Motor Yacht Charter offers 4 to 15 days cruises in the Leeward Islands (Huahine, Raiatea, Tahaa, Bora-Bora and Maupiti).
More information. Large cruise ships also offer cruises to French Polynesia's various archipelagos: The Gauguin, the 2 Princess Cruises ships, etc...
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To go to the Austral Islands: a freighter with passenger cabins, the Tuhaa Pae, ensures transportation there twice a month, with a trip 24 to 36 hours long. This also is a fascinating experience to live in the friendly company of some cheerful bunch partying on the way back home. Singing, typical food and garanteed ambiance will be part of the trip.
To go to the Marquesas, the freighter's cruise, Aranui, is a unique and much appreciated experience with many activities planned in each visited island. (Rates: between 1,500 and 2,500 Euros, European plan). Departure either from Tahiti, or you can fly to catch the Aranui directly in the Marquesas and take the cruise right there. The return to Tahiti can be done by plane or on the ship (a 4-day crossing) for 180 Euros one-way. www.aranui.com 

To go to the Tuamotu-Gambier Islands, to reach the remote atolls of the Tuamotu, a few fishing boats (the Cobia, the St Xavier Marie Stella or the Rairoa Nui), equipped to accomodate 4 or 6 passengers, offer limited but acceptable service. Rates: a sleeping berth starting at 75 Euros a week.
The flotilla of the Taporo and Vaeanu ships also provide regular transportation to the Tuamotu,Marquesas and Leeward Islands.