Here’s a cool Java applet that lets you do pretty sophisticated digital simulation. There’s a variety of components available and even a “logic analyzer” that you can use to view the results. You can even hook up switches and LEDs that you can manipulate on the screen.

There are several other similar applets available but this one seems to be the most full featured that I’ve found.

If you prefer to run on on your own computer, have a look at http://web.mit.edu/ara/www/ds.html which is free for student use, at least, and somewhat shareware (the author solicts a range of contributions) for everyone else. The program is clearly “older”, but it functions fine.