These aren't mine, but easily my most used After Effects expressions.

"If you've ever animated these sorts of things manually, you'll know what I mean. Most will need to be tweaked to your specific needs, but it's just a matter of playing with the numbers a little, and understanding how they'll change your animation."

Jumpy Wiggle 1 makes wiggle skip and hold rather than move fluidly.

// Jumpy Wiggle 1 (moves at a random FPS)
v=wiggle(5,50);
if(v < 50)v=0;
if(v > 50)v=100;
v

Jumpy Wiggle 2 is similar to 1, but works at a defined FPS so your "jump" will happen at a regular pace.

// Jumpy Wiggle 2 (moves at a defined FPS)
fps=5; //frequency
amount=50; //amplitude
wiggle(fps,amount,octaves = 1, amp_mult = 0.5,(Math.round(time*fps))/fps);

Inertial Bounce is like making your moves "rubbery." Layers will overextend, then settle into place on position and rotation keyframes.

// Inertial Bounce (moves settle into place after bouncing around a little)
n = 0;
if (numKeys > 0){
n = nearestKey(time).index;
if (key(n).time > time){
n--;
}
}
if (n == 0){
t = 0;
}else{
t = time - key(n).time;
}
if (n > 0){
v = velocityAtTime(key(n).time - thisComp.frameDuration/10);
amp = .05;
freq = 4.0;
decay = 2.0;
value + v*amp*Math.sin(freq*t*2*Math.PI)/Math.exp(decay*t);
}else{
value;
}

Sometimes you just want something to move constantly without keyframing it. Use throw.

// Throw (move at a constant speed without keyframes)
veloc = -10; //horizontal velocity (pixels per second)
x = position[0] + (time - inPoint) *veloc;
y = position[1];
[x,y]

Same as throw, but for rotation.

// Spin (rotate at a constant speed without keyframes)
veloc = 360; //rotational velocity (degrees per second)
r = rotation + (time - inPoint) *veloc;
[r]

by Chris Wright