Unclaimed islands may be griefed, you should only really spend time on unclaimed islands for collecting resources, unless you don't mind risking being raided and having your home turned up-side-down. You can find a random island by using /rand.
Note: /rand can occasionally take you to a claimed island, you can either swim to another island or simply run the command again after the timer runs down.
If you wish to become a bit more independent, you may want to claim an island of your own, instead of settling on someone else's. This can be done with the use of bedrock, which can be purchased in game from another player or from our donor store for $7.50. Although governing an island may sound like a walk on the beach, it often is not. You need to be able to defend your island, as it can be blockaded!
There will only ever be six Royal Islands. It is not possible for an island to become Royal from being a claimed island. What these islands do is play a vital role in the economy, mostly. They are "public" islands, where shopkeepers can open their businesses, shipwrights can sell their boats, and where players can find a safe place to live.
Royal Islands can be blockaded, and it is the only way of obtaining one. Inhabitants of the island are not effected by these blockades, apart from the fact that one governor may be better then the other, and ideally you want to live on an island where your governor is constantly adding new content.
Cursed Islands are "adventure" islands. Here you can choose from the two types of activities, being the "plunder", or the "boss battle". The plunder awards players with a fair amount of loot, such as diamonds, emeralds and so on, while the boss battle awards players with fist fulls of wealth... if they're lucky, and if they actually defeat the boss!