Some simple games I started out with are Space Invaders, Pong, Columns and Tetris. They provide a simple intro to a lot of programming concepts and are not heavy weight, certainly clones of these games can be written quickly. I would consider a Mud (networking + multiple players) or anything with 'physics' a bit too heavy as an 'introduction' and more suited to a 201 or higher course.

n!

Not really a game, more like emulator - show your students how funny physics can be in the gaming manner.

Imagine the mobile app where you can spawn particles at any point of the screen and they immediately fall down on the floor by impact of gravity (which you can grab from mobile accelerometer) and jump back, by inverting and fading the impulse at the point of collision with the floor. You can utilize forces, impulses, accelerations and speeds in this simple application, also collisions and so on. You keep spawning them and rotate your screen - those particles follow your gestures by recalculating their physics properties in real time.

The magic mysterious world of formulas becomes very simple and clear, when you see their applicative nature in a simple mobile app =)

Rather than list games, I think a beginner is more motivated doing fun interactive graphical cool stuff and important game logic rather than feel overwhelmed they need to make a game.

Game feature to get your feet wet with 2D Graphics Coordinate System and game logic all at once

1) Just getting the image on the screen is probably the first thing any beginner to do!

2) Game Object movement tests your understanding on 2D Graphics Coordinate System super fast! Introduces the beginner to event listeners, key and mouse!(Super fun stuff) (Super useful for pong, breakout, space game)

3) Animation - this feature has intermediate difficulty. If the codebase is done cleanly, it can be reused as a animation system. This feature teaches adding images to a list and iterating the list through while evaluating frame counter comparison and drawing images on the screen.

4) Game State Management- this can be a character moving, running and having an animation system draw the appropriate animation relative to the character state. This can also be the behavior of the game itself(is the game over, is the game in main menu or in the overworld?)

5) Dialogue System - this feature will definitely take the cake as being as a larger feature and will make a teacher super amazed. This feature promotes creative thinking, string manipulation, handling more art assets.

6) Inventory is a good idea. Get them aquainted with lists and arrays. Deleting or adding items.

Rule of thumb: Always tell student to start small!

I think one of the first games I did was I guess you could say a console style text game (it was done on a C64) where you start in one "town" and buy stuff, then go to another town and try to sell it at a profit. Make enough money and you can expend your capacity to carry stuff. Every time you moved from one town to another the prices for things at each town would fluctuate a bit.

Asteroids, or variations of it, are pretty fun to see in action, and tend to involve some simple physics and either vector or angle math.