When was a program, transaction last used? How to know which users are using which transaction or executing which program? Which are the most frequently used programs or transaction?

To know how many users are viewing and maintaining a particular transaction use transaction 'ST03', in3.0x :-

• Performance database
• Select instance
• Select desired period
• Choose Transaction profile

To find the Frequently Used Programs or Transactions in 4.6x :-
ST03 ---> Detail analysis Button --> Under Global - One recent period then select day or week or month ---> Transaction profile Button
In 4.6x, you can also try the new Workload Analysis tcode 'ST03N'.

The SAP standard retention period is 3 months.  You can change the Standard Statistics via clicking :-
Goto -> Parameters -> Perfomance Database

To analyze the Statistics by users for transactions and programs use transaction STAT

STAT looks at the STAT file created by each SAP Instance.

It is by default 100 MB.  Every hour there is a COLLECTOR_FOR_PERFORMANCE job RSCOLL00 aggregating this data into MONI table.  It will truncate STAT file once the specified  limit is reached.

So, you can see details for however many days in this 100 MB using STAT, or ST03 to see the MONI aggregated data.

To change the 100 MB limit, ST03 -> Goto -> Parameters -> Performance Database.