You don’t have to run the full installer each time to create a database, but you can only create one database at a time. For each additional database you can run dbca to create a database from a GUI based program, or create a new database from sqlplus using the <b>CREATE DATABASE</b> statement. Use the GUI if you can.
Oracle uses the term instance to represent the part of the database that the end user knows as the place there data is stored, and the database is the server side programs that make it available. During an install Oracle ask for the location to install these database file and that is known as the ORACLE HOME, of which you can have more that more.
From your question I am not clear want you are trying to achieve. Are you wanting to install Oracle 10g multiple times on the same server to provide 10g to different client groups that require autonomy as in they may be different customers onan ISP host; or do you want more than one end user database as a Dev, Test & Prod?