I've spent the last couple of months trying to find real data (not simulated) of a longitudinal study, but I can't seem to find one. Any topic and time frame is fine, but the dependent variable must be binary, and a few covariables are also desirable. I appreciate any help immensely!
(1) The statistic software R comes with a number of datasets. You can see which datasets are available with the command
data(). Here is an overview.
Among the datasets that came with my distribution of R is the dataset
Titanic, which includes the binary variable "Survived", which gives information about which passengers survived the Titanic's maiden voyage.
UCBAdmissions, gives information about which applicants were admitted or rejected to UC Berkeley.
The data in both datasets is grouped (by sex etc.). Both are not longitudinal, though.
You can get information on each dataset with
?Titanic. Maybe more datasets include binary variables.
(2) As Jeromy Anglim noted, many statistics text books offer an online data repository. Here is the one for Applied Regression Analysis and Generalized Linear Models (2nd ed.) by John Fox. Here is the one for Statistik (7th ed.) by Fahrmeir et al. (in German).
Perhaps have a look at chapter 14 of Gelman and Hill http://www.stat.columbia.edu/~gelman/arm/
Chapter 14 is on multilevel logistic regression and the website provides access to all data files used.
I just don't have access to the book right now to tell you which of the many datafiles used in the book correspond to the examples in chapter 14.
More generally, textbooks are a good way of directing your search. Many provide practice datasets. So you just need to find textbooks on longitudinal analysis of binary response data.