In Terminal:
system_profiler SPApplicationsDataType
If you want to programmatically extract data from that, add a -xml option to get the output in XML format, then use XML tools of your choice to extract the data. (Trying to extract data from a complex non-XML file using regular expressions is iffy at best.)
If you want to save the data for later perusal, save it as a .spx file (in XML format). Then use System Profiler itself to view the file pretty-formatted:
system_profiler -xml SPApplicationsDataType > ~/Desktop/apps.spx
If you want to see what has changed between different dates, use diff or equivalent to compare such files, saved on those dates, to see what's changed.
