Hello and welcome to Tom's Hardware forums. Yes, it is stored in your router and to get there, go Start then Run in XP - Windows key plus R in Vista and Windows 7, then type in the following, including all the spaces:-
cmd /k ipconfig /all
then press Enter and from the black form that shows up, take a note of the numeric code beside the Default Gateway icon - something like 192.168.0.1.
Type exit to close the black form.
Open Internet Explorer and enter that code into the URL address bar as though it was a website. You're then at the login page to the router's settings utility and admin will usually be the login with either admin or password as the password.
If you're in, seek out Wireless and then Security and take a note of the key. Sometimes it may be a passphrase, some a simple set of letters and others a hexadecimal code. You also may as well note which level of security it is - WEP, WPA or WPA/PSK 2 and then either AES or TKIP. Your computer will already know this but it's handy information to store. Note also that hexadecimal only contains numbers from zero to 9 and letters a to f so there's no confusion of I and O with 1 and 0.
Keep a note of that security key in My Documents and also outside the computer.
If you need more help when this thread has been inexplicably closed down, feel free to PM me.