How can I see where a program writes to my disk? If I want to uninstall a program and remove all trace of data it stored on my computer, 
is there a tool to see where a program has written data? I expect it isn't going to be possible after the fact, but perhaps there is something that can run when a program is first launched to monitor all the locations to which it writes?

I think I'm looking for something that does for local storage what Little Snitch does for the internet.
If I get it right, you want to monitor all file-system operations of your app when you launch it and when it's running ?
Rather than finding each and every byte that this program has ever written to your hard-drive.  

For the first case I have two recommendations:


fseventer





Instruments.app from /Developer/Applications/ (you need Xcode for that)


Choosing "File Activity" from the templates





Supplement from 2011-12-22


And for the command-line, copied from here  

sudo opensnoop -p PID


Shows you all of the files that are being accessed on your system by a particular process (by passing its PID)