In order to distribute a function I've written that depends on other functions I've written that have their own dependencies and so on without distributing every m-file I have ever written, I need to figure out what the full list of dependencies is for a given m-file. Is there a built-in/freely downloadable way to do this? 

Specifically I am interested in solutions for MATLAB 7.4.0 (R2007a), but if there is a different way to do it in older versions, by all means please add them here. 

For newer releases of Matlab (eg 2007 or 2008) you could use the built in functions: 

1. mlint
2. dependency report and
3. coverage report 
Another option is to use Matlab's profiler. The command is profile, it can also be used to track dependencies. To use profile, you could do 

>> profile on   % turn profiling on
>> foo;         % entry point to your matlab function or script
>> profile off  % turn profiling off
>> profview     % view the report

If profiler is not available, then perhaps the following two functions are (for pre-MATLAB 2015a): 

1. depfun
2. depdir 
For example, 

 >> deps = depfun('foo');

gives a structure, deps, that contains all the dependencies of foo.m. 

From answers 2, and 3, newer versions of MATLAB (post 2015a) use matlab.codetools.requiredFilesAndProducts instead. 

EDIT: 

• Remember that the Profiler will only show you files that were actually used in those runs, so if you don't go through every branch, you may have additional dependencies. The dependency report is a good tool, but only resolves static dependencies on the path and just for the files in a single directory.

• Depfun is more reliable but gives you every possible thing it can think of, and still misses LOAD's and EVAL's.