If you're a beginner, Access or using an Excel spreadsheet is your best bet I'd say.
If you have some experience (especially with SQL), MySQL is a great SQL-based server:
http://www.mysql.com/.
A great package for MySQL is phpMyAdmin, which allows a GUI for editing/maintaining your database/tables. You need to have a web server installed with php support:
http://www.apache.org/ - Apache (Web Server)
http://www.php.net/ - PHP
http://phpmyadmin.sf.net/ - phpMyAdmin
There may also be specialty programs/databases out there made for the type of data you want to keep (a catalog of video games).
Good luck!