Free circuit simulator for educational purposes

I often use the falstad simulator: http://www.falstad.com/circuit

It's a Java applet, so will work on pretty much any operating system. The interface does take a bit of getting used to, and there are problems saving in Linux (it gives you a link to copy and paste, and copy and paste in Java doesn't work too well in Linux).

Other than that it ticks all your boxes. It also has some good sample circuits. A Windows version (circuitmod) is based on this.

CircuitLab is a beautiful in-browser circuit simulator that was launched a few days ago by a pair of MIT students. I think electronics.SE is going to love it! It does full mixed-signal analysis and appears quite capable. I look forward to seeing where it goes!

Here's a screenshot:

You can share circuits via convenient short URL's. For instance, here is the circuit shown in the schematic: http://circuitlab.com/circuit/fq7c97

I like LTSpice you can find it here: http://www.linear.com/designtools/software/ It does jsut about everything.