Although you have mentioned that you are working on a web application, you have not even given us the slightest hint as to what are you using in that web application, is it JSP, Servlets etc.
Yes its perfectly possible, although restricted to the list of users logged in since the last time your web application was reloaded or your web server restarted, if you want it to persist even across that, then its got to be a DB or a File to store that info.

In the former if using a JSP,you want your HashMap object to be visible across multiple sessions it will have to be in the "Application" scope.
Alternatively if you are using servlets, you could have your HashMap initialised in the init() method of your Servlet, and then just keep adding the list of Users logging in, in your corresponding service() or doGet() or doPost() method whichever you are using.

thanQ vry much