I will put a girdle round about the earth
in forty minutes

is a claim by Puck in A Midsummer Night’s Dream by William Shakespeare.  Has anyone worked out his speed?  A supersonic fairy!

The best of both worlds is apparently regarded as being an impossible objective.  The two worlds could be heaven and earth.

Worlds apart means very different.

A lie can be halfway around the world before the truth gets its boots on is a saying I do not remember from my childhood.  I came across it much later.

The most important thing in the world is usually used in the negative.

It’s a small world is often said when unexpected connections are made between people or places.  Everyone has their own stories of meeting the friend of a friend.

It’s the way of the world.
This is a generalisation about the way life is conducted.

To the ends of the earth is as far as it is possible to go.

There are plenty of songs with world in them.  Two which spring to mind are Wonderful world and He’s got the whole world in his hands.

Search the length and breadth of the land is something fairy tale princes used to do looking for a bride.

East, west, home’s best is sometimes displayed in houses.

In my neck of the woods means where I live, whether or not trees are growing there.   Interesting use of the word neck.  The Concise Oxford Dictionary gives this the meaning of (remote) location.

A prophet is without honour in his own land.
Matthew 13:54-58