If you have retained proof of purchase, these places may be able to provide you with a new activation code for your game. If you have lost your activation code for a copy of 'The Sims: Castaway Stories', you may want to try contacting either the retailer you purchased it from, or the game publisher. This loss of finance has huge ramifications for game publishing companies, and as piracy increases, more and more game producers are likely to close down as they cannot afford to pay their coders. Without an activation code, numerous people would be able to play a game from one disk passed between friends, or a disk image distributed via the internet, and the company behind the game would suffer hugely.
The reason the codes are included with the packaging is to prevent piracy and reselling of computer games. If the game is downloaded from a legitimate source, the download should include an activation code. Activation codes for PC games for both Windows PCs and Apple Mac computers are usually included inside the packaging of the games themselves.