1.15: Gateway games - the first one's free

Gateway games--I'm sure I've mentioned this term multiple times on this blog.  I've probably given a definition as well, but for the sake of discussion, let's define "gateway game" again.  The term refers to a game that interests a person in gaming, and for our discussion, may introduce a person to modern boardgames.  Many boardgamers can recall their gateway game, and many people cite the same gateway games (often Eurogames) for good reason.  But what makes a good gateway game?  As I see it, a gateway game should have four elements:

A Gateway game:
1.  Has a simple rules set
2.  Is easy to understand
3.  Is easy to play
4.  Is engaging.

The combination of the first three makes the game accessible, the last makes a person want to play.  I'll go through each of these and give examples.