The map of the world that we are most familiar with is the Mercator Projection. Developed by Gerardus Mercator in 1569 as an aid in navigation, and functioning quite well at a local scale, it has some serious flaws as a means of representing the entire globe.
It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments which conserve the angles with the meridians. While the linear scale is equal in all directions around any point, thus preserving the angles and the shapes of small objects (which makes the projection conformal), the Mercator projection distorts the size and shape of large objects, as the scale increases from the Equator to the poles, where it becomes infinite.
One of the issues becomes obvious with the superposition of Greenland over Australia showing their actual relative sizes.
Even knowing this, it is almost impossible for most of us to visualize a flat map of the world in any other way. Wikipedia has a list explaining a number of other projections with some of their advantages and disadvantages.
For the map geeks among my friends and relatives and anyone who wants to see the world from a different perspective. Mercator Extreme is a project that explores the extreme distortions of this projections from different points on earth.