I want to delete some installed games, in order to free HDD space. Can I simply drag the application to the Trash? Will this delete all the files related to the game? Saved games included? Or do I have to perform a complete uninstall?
That's going to depend a lot on the game. Some games are relatively self contained, though most will at least place preference files in ~/Library/Preferences/. It's also not uncommon to find files in ~/Library/Application Support or even in ~/Documents. GGJStudios will pop in here soon with his manually uninstalling guide, but that'll get you started.
I want to delete some installed games, in order to free HDD space. Can I simply drag the application to the Trash? Will this delete all the files related to the game? Saved games included? Or do I have to perform a complete uninstall?
If you just want to delete the app, drag the .app file to the trash. No other software needed. If you want to completely remove all associated files/folders, the most effective method for complete app removal is manual deletion: