I use Desmos, an interactive graphing calculator, to teach all the time.  Usually it's a quick demo and I don't even feel the need to save.  But sometimes it gets more involved and I keep the results for later.  Here's some of what I've collected:

Secant-to-Tangent:  Useful for one of my all time favorite concepts to teach: "what IS a derivative?"  In this plot you can choose your favorite function, pick a point of tangency, and then shrink h and watch with greatest satisfaction as the secant meets the tangent.

Taylor Series:  Increase the number of terms, p, and be amazed as the approximation fits the sine curve!  You can only adjust p in this one, not the function.

Fourier Series:  Similar to the Taylor Series, increase p and watch the magic.  Here you can play with different functions too.  You can observe Gibbs Phenomenon, think about even and oddness, gain some intuition about the effects of discontinuity and non-differentiability, and more.  Note that I've only plotted a few periods of the function, so either add more yourself, or just don't zoom out too far.

Parameterization:  A personal favorite of mine (though hard to explain)!  This was an attempt to demonstrate the importance of parameterizing by arc length when I taught vector calc.  Hit the play button next to "s" in the upper left, and watch the dots move around the circle (you can also click on the red and purple dots are the far left to toggle them on and off.  It helps to watch them one at a time).  The idea is that both of these parameterizations produce the same curve, but if we tried to calculate things like curvature by taking derivatives with respect to time, we'd get different answers.

Wave Velocities:  I didn't make this to teach any students.  I made it to teach myself, and I love it!  It demonstrates the difference between group velocity and phase velocity in waves.  Hit the play button for t (upper left), and watch as individual wave peaks move to the right (positive phase velocity), but larger wave packets move to the left (negative group velocity).  You can also change those velocities.  I'd recommend just doing that with the slider controls, not the play buttons.  That being said...  I dare you to hit all 3 play buttons together :)