These are some great data sets to get through the mechanical nature of statistics. It's not very current data but it's great for practicing statistical methods.
For the longest time this set of data was not available but just recently it was hosted by Data Description Inc. so now we have access to it again.
AnalysisThere are far too many sets to talk about analysis but when the site was down I blogged about one of my favourite sets on Smoking and Cancer. Take a look at that post to get a sense of the data. When you get to any data set, to see the actual data file, click on the Datafile Name
This will show you the text file of the data with the download link at the top of the page.
From that point you can do the analysis. Each data set will have a detailed description of each variable and a short story and sample analysis of each set
There are many data sets on this site for every statistical topic and on a range of subjects. One thing you might have your students do is just explore on this site and find data sets that can be used to exemplify a particular statistical concept.