There are currently 25 different laboratory demonstrations of classic studies in cognition, perception, and social psychology, with more added all the time. Your whole class can participate, and then download their own data and analyze it. They can also download the data from students at other schools and compare. Data are organized, using very nice macros written by the PsychExps team into Excel spreadsheets. You can analyze from there, or import into SPSS. Most demos have Teacher Guides associated with them. They even have the Implicit Attitudes Test (IAT) that is becoming so popular. I use this site regularly for my Research Methods class.
Finally, there are also a number of "real" experiments in which researchers can collect their own data using the services of PsychExperiments. Don't overlook these -- some are pretty darn interesting, even if they're not yet "classics."
You must download Macromedia's Authorware Player (like Shockwave, but a little different). It's easy to do, and the player is self-updating, so after you do it once, you never have to again. Links at PsychExperiments take you directly to the download page, so no problems!