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When I sit down to prototype something new I always find myself looking up the same snippets to do the same types of things. I figured I might as well record them somewhere so I know an easy place to look when I do forget. All the samples will be in Javascript and should be able to be easily converted to any other language.

Distance Formula

Obviously a pretty important one, used to tell the distance between 2 objects. Can be used for simple radius collisions as well.

var distance = Math.sqrt((x2 - x1) *(x2-x1) + (y2 - y1) * (y2-y1));

Move toward an object (Without rotation) with easing

x += (targetX-x)/speed;
y += (targetY-y)/speed;

Angle Based Movement

I always see myself needing this one, whether its for an Asteroids clone, or a follow the leader type game.

velX = Math.cos((angle * Math.PI / 180) * thrust);
velY = Math.sin((angle * Math.PI / 180) * thrust);

Friction

How do I make something slow down if no force is applied?

velX *= .98; //Any val under 1 is suitable for your needs
velY *= .98

2D Matrix

This is a pretty simple one I know.. but I always seem to forget it. This is how to store a 2d matrix in an array. And how to find a value you need.

// 2d matrix[y * width + x]
var arr = [],
     width = 10;

for(x=0; x<width; x++){
    for(y=0; y<width; y++){
        arr[y * 10 + x] = x + y; //Or whatever value you need to assign
    }
}

//Retrieve a value from x:5, y:2
var val = arr[2 * 10 + 5];

Move towards and object at a constant speed

    var tx = targetX - x,
        ty = targetY - y,
        dist = Math.sqrt(tx*tx+ty*ty),
        rad = Math.atan2(ty,tx),
        angle = rad/Math.PI * 180;;

        velX = (tx/dist)*thrust;
        velY = (ty/dist)*thrust;

Example