Let's say I have some items that I want to categorize. I have a categories table that contains the category id and name. Would it be better if I:
A) Added a field called 'category' to the items table that contains the category id it belongs too
B) Created a new table that contains a game id and a category id ti show which game belong to which category
General rule of thumb: the more joins your query has, the more slower it runs. Thus second option will be somewhat slower, but it will provide additional functionality which first option coudn't provide.
I will always choose normalization over performance. Hardware is simply cheaper than man power (aka the cost of maintaining and developing a poorly structured database).