Yes you do depending on what type of software license you originally
bought. If you bought your original license from an OEM i.e. from
companies like DELL, HP etc. then you need to buy a new license every
time you change your system.
However, if you bought a retail license, i.e. software in a box from
retailers like Amazon or PCWORLD etc. then you don't. You just have to
install it on a new system using the media provided in the box and TRY
to activate the software online. If it fails then you need to phone MS
in your country, (you get toll free number on the screen) and explain to
them what you have done. They will provide you with some numbers over
the phone which you need to enter on your new system to activate.
If you had Students license, then again there are some restrictions but
I am not going to explain them here.
Hope this helps.