Comparing 2 nominal variables I would like to compare the nominal variable (if an individual had fallen) with other nominal demographic variables, such as gender. 
Besides cross tabs, is there any other statistical tests I can perform to explore the relationship between nominal variables?
Thanks!
EDIT TO ADD MORE INFO:
I am looking at relationships between history of falls in the previous 12mos (dichotmous variable Yes/No) and a series of demographic factors. Is gender associated with previous fall history for example. Other variables include the use of mobility and low vision aids, living arrangements, if individuals take 4 medications or more, if individuals walk outside for 15mins or more at least once a week.
I have investigated the relationship between fall history and other clinical and demographic ordinal or continuous data, but the nominal variables remain and I am unsure what I can do with them.
Thanks again,
H
 A: Cross Tabs allows you to visually check for a pattern in the nominal data. On it, you can run a variety of $Chi^2$ tests (Pearson's being the common) which will enable you to check whether the observed distribution of values between categories significantly differ from the expected ones. On to of that, you can perform a measure of the strength (0 to +1) of the association between the variables such as $Cramer's V$.
If the variables were ordered, you could measure correlation using $Spearmans$ correlation test, yet the variables you mentioned are not ranked. 
Edit: Logistic Regression - Considering you have numerous variables (whether binary or interval), you might want to perform logistic regression to check the odds ratio of your dependent variable based on several covariates simultaneously.  $Chi^2$ and $Spearman$ test allow you to test only relationships between a pair of variables at a time. For a more holistic approach, logistic regression enables you to test for relations while controlling for confounders. This approach can let you know how the various variables affect falling together.
for tutorials on logistic regression see in: SPSS, R, Stata or SAS
Hope this helps.
