I applied for F1 visa and got the visa. Few weeks later I got married and the University is sending an I-20 for me again under the same SEVIS number adding a dependent and another for my spouse. What do I do with my old I-20? Do I have to inform the embassy that I have received a new I-20? Do I have to pay the SEVIS fee again?
It is quite common for you to receive new I-20 forms throughout your academic career. For instance, you'll receive a new one if you change your major. You do not need to do anything except remember to use the new I-20 instead of the old I-20 when traveling (and, if you're already in the US, have the I-20 endorsed for travel).
You don't need to give the new I-20 to the consulate unless you need a new visa. But you will need the new I-20 at the border to enter the United States.
As for old I-20s, you should keep these in a safe place, as they may be required for certain things (such as OPT, or H-1B visa applications).