This article covers the different beverages found within the series.
It should be noted that the word "sake" is used often in the One Piece series to refer to alcohol in general due to that being how the Japanese language works. However, as English has adopted "sake" into its lexicon to refer to nihonshu, it is actually a mistranslation to refer to all alcohol in the series as "sake", because in English, "sake" refers exclusively to "nihonshu", while often it is another form of alcohol being discussed.
In the series, rum and other alcoholic beverages are prevalent throughout the series. In the real world, water was impossible to take on long journeys as improperly stored water goes stale within days and leads to water poisoning and other diseases. Alcoholic drinks were seen as a cheap alternative as they did not turn stale like water and can last for much longer (in many cases years) as well as a cheap leisure pursuit and social drink. Oda himself continued this tradition with his own story and even provided explanation for why certain drinks were linked to pirates in one SBS. One of the more prominent cases is the song Binks' Sake which is a typical pirate song about delivering alcohol. The first reference to drinking alcohol came from Shanks in Chapter 1 (anime Episode 4) and Higuma's incident at Partys Bar in Luffy's hometown.
In the 4Kids English dub, any references to alcohol were altered to "juice", in line with their toning down of the anime for a younger audience. The uncut FUNimation dub, however, keeps all references to alcohol intact.
Rum (ラム Ramu?) is a strong alcoholic drink that has been historically linked with pirates and sailors. It is distilled from sugar cane and thus was abundant in the heavily pirated Caribbean. Rum in particular was one of the cheapest alcoholic drinks for purchase and was bought by the barrel.
Rum was also the official drink of the British Navy; this was originally brandy, but was later changed to rum simply because it was cheaper.
Nihonshu (日本酒 Nihonshu?) is a particular type of traditional Japanese wine brewed from rice. However, English lexicon has, over time, adopted the Japanese word sake to refer exclusively to "nihonshu". Nihonshu is easily distinguished from other types of alcohol by the traditional white bottle and traditional method of drinking it, sipping it from small dishes, rather than from mugs, bottles, or cups.
Sake is seen being imbibed at several points during the series, but is rarely named as such. The first time it is definitively seen being drunk is during Shanks time in Partys Bar. It should also be noted that Gaimon's home-made alcohol he and Buggy shared during Buggy's mini-story arc appears to be "sake" as they drink it from dish-shaped holders rather than full-on cups. The last drink that Whitebeard and Roger had with each other was sake. Vasco Shot carries a calabash gourd of sake with him at all times, earning him the nickname "Heavy Drinker".
Shanks, who has traveled the world, thinks his hometown in West Blue makes the best "sake" in the world.
Jerez is Z's favorite type of alcohol. Kuzan gave him a bottle of it, which Zephyr later drank just before his final fight with Luffy. It is sold in 0.75L bottles and produced in Sherry. This is a pun on sherry (known as Jerez in Spain), a wine produced in the city of Jerez de la Frontera in Spain.
Déesse is a brand of alcohol, apparently red wine. When a 25-years old Donquixote Doflamingo woke up from a nightmare of being lynched by a mob during his 8-years old childhood, he gulped down a bottle's worth sloppily to cool his head, dripping some on his chin, and then tossed the bottle and what little remained in it to the ground before picking up a ringing Den Den Mushi. "Déesse" is the French word for "Goddess".
Water is transparent, odorless, tasteless liquid. It's a vital substance to all forms of life.
During the Alabasta Arc, water was the main driving force of the conflict between the Alabastan King Nefeltari Cobra and the Rebel Army led by Kohza due to the lack of rain caused by the use of Dance Powder, an illegal substance that forces artificial rain to happen in a certain location in detriment of natural ones happening on neighboring places.
It was later revealed that this scheme was all orchestrated by the then Shichibukai Crocodile, who not only started an entire conflict that he could exploit to achieve his goals, but also managed to prevent water, which is the main weakness of his Suna Suna no Mi, from being used against himself. Luffy, however, would be able to use water against him in their second encounter.
Mineral water is natural spring water, usually with additional compounds mixed in depending on where it is sourced from. It is commonly sold bottled, and drunk for health benefits.
Juice is a general name given for non-alchoholic drinks extracted from fruits and vegetables.
In the very first chapter of the series, Shanks offered Luffy a glass of juice at Partys Bar. Juice is also abundant in Totto Land, where several islands have rivers made of varying flavors of juice.
Vegetable Juice is juice extracted from various vegetables. Franky consumed this by accident during his fight with Fukurou at Enies Lobby, causing him to feel healthy, but not actually powering him up.
Melon Juice is juice extracted from melons. The Seducing Woods have a river made of this kind of juice, where a crocodile homie lives.
Using her Devil Fruit abilities, Charlotte Smoothie is able to make any sort of juice consider her target. So far, she was shown making juices from Renaissance, lava from Mauri Island, a maiden that stabbed a 100 men, and a giraffe that cries strangely.
Cola is also an essential source of energy for the Straw Hat crew member, Franky. As a cyborg model "BF-36", Franky is able to store cola in a mini-fridge he has where his stomach would normally be, and he can store up to three bottles (6 liters) of cola. Depending on the amount of cola he has stored, his attacks can be a lot more powerful, and they are weaker when he has less cola; it is unknown if his new model "BF-37" is the same, though he still uses cola as power. The Straw Hats' ship, the Thousand Sunny, also uses cola for attacks and extreme maneuvers.
Coffee played a role during Ace's Great Blackbeard Search, where the Marines from the G-2 Marine Base commanded by Vice-Admiral Comil were having problems drinking their coffee, which they considered too bitter. This problem was solved after Portgas D. Ace delivered a letter from Moda, a milk-maiden and daughter of the base's chefs, to Comil, which allowed the base to get a steady supply of milk in order to put it on their coffee, making it taste much better.
Charlotte Pudding had also brewed tea while serving the Sanji Retrieval Team at her cafe.
Green Tea is a somewhat mild type of tea. During the Vinsmoke Family lunch with the Charlotte Family a homie canister of Green Tea has offered to make Sanji a drink. The canister was present when the Vinsmoke talk about their plans after the wedding.
Black Tea is a somewhat strong type of tea. During the Vinsmoke Family lunch with the Charlotte Family a homie canister of Black Tea has offered to make Sanji a drink, which he took. The canister was present when the Vinsmoke talk about their plans after the wedding.
Black Tea was confirmed to be Sanji's favorite drink. 
Milk is liquid extracted from mammals such as cows. It can be served as a drink or as an ingredient for other dairy products such as cheese.