I know Wizards can't apparate where they want on the Earth, except if they are very powerful but what about a house-elf ? Their magic is different so I was wondering if they can apparate wherever they want or if they have a limit too.
J.K. Rowling has not yet clarified on the exact "science" regarding House-Elves Apparition but we can make some rational assumptions with canon examples:
- House-Elves can Apparate without a wand and (probably) without any form of license.
- House-Elf Apparition is not bound to the same restrictions as the wizards's counterpart (e.g. Kreacher was able to Apparate to the cave where Voldemort hid his locket-Horcrux, although the Dark Lord has placed a powerful Anti-Apparition charm). There are places where House-Elves can Apparate and wizards cannot (e.g. Hogwarts).
- House-Elves apparently ought to know the interior place of the target location prior to the Apparition or they should have traveled there at least once (e.g. if that wasn't the case, Dumbledore would have used a House-Elf to enter the cave of the locket-Horcrux and would not spent so much time in locating it across UK).
- House-Elves cannot Apparate to places that are shielded by the Fidelius Charm (e.g. Dobby managed to Apparate near Shell Cottage and not inside the house).
- House-Elves cannot bring other wizards with Side-Apparition into properties that are shielded by the Fidelius Charm, provided that the Secret-Keeper has revealed the address to them -meaning that they can travel to there (e.g. Kreacher couldn't and apparently didn't bring Belatrix inside Grimmauld Place 12, when it served as the Headquarters of the Order of the Phoenix although he has been provided with the address by Dumbledore).
- Side-Apparition works with House-Elves as with wizards (e.g. Dobby brought Luna, Mr. Olivander and Dean to Shell Cottage).
For a more detailed analysis on the third bullet, take a look at an old answer of me on "Why didn't Dumbledore ask the house elves to search for the Chamber of Secrets?"