The Padron, what it is, why you need it, and how to get it
The Padron is an administrative registration for residents of a municipality. It proves residency in the municipality when you live there (note, this is not proof of Residency, that is a legal concept, it proves you live permanently in a municipality (town, village, city). If you live in more than one place in Spain then you register where you live the most time.
You should only apply for a Padron if you live full time in Spain, the actual Spanish states: Toda persona que viva en España está obligada a inscribirse en el Padrón del Municipio en el que resida habitualmente. (All persons who live in Spain are obliged to apply for a Padron if they live full time in Spain).
The Padron proves how many people live in a municipality, this is needed to see how many resources an area needs and how much income from tax etc and area should provide. In this sense think of it as a census.
You need to have a Padron to vote in local Spanish elections, and European elections (Many thanks to those who corrected my assumption that it entitled the holder to vote in National elections, it doesn't).
To enroll your children in a local school you will need a Padron.
You cannot become a Spanish resident without having a Padron, and without Spanish residency you cannot get Spanish healthcare.
You need a Padron to change your driving licence to to a Spanish one.
Many people fear that as soon as you have registered as living full time in an area, by applying for a Padron, you will beome liable for tax, in fact whether you have a Padron or not you become liable to register for Spanish taxation after just a couple of months of living there full time, so there is nothing to lose by registering, but of course by the acting of signing up for one you are implying tax residency and liability.
But where do you get this magical registration from? Well that is simple, from the Town Hall, and each Town Hall has slightly different requirements. You will at the very least need your passport and one copy (take two, just in case). You should bring along any rental contracts, house deeds, utility bills.
The main thing is to ask them at the Town Hall (Ayuntamiento), they want as many people to be on the Padron as possible, so will be very helpful.