Each island has it's own forms of incomes depending where you're at for each one
In Desert ~ Auto cactus farms (Must be online for them to grow and drop)
In Birch ~ Melons is your best source of income
As you progress you get iron so you can make an auto afk mob farm (mobs dying from fall damage)
In Savannah ~ Pigs and Skeletons
In Extreme Hills ~ Creepers
Once you hit Swamplands, you have access to lava
Swamplands ~ Slimes
Currently Most Popular End Game Farms ~ Cooked Pork chops(Pigs) and/or Slimeballs(Slimes)
(
Logs are also a good source of income but as you progress they take an eternity to grow)