As you may have already noticed in Poland, any time you try and do something (such a open a bank account or get a mobile phone contract) people ask your for your 'Pesel'. Most of the time you don't actually need a Pesel if you argue with them - but of course it's a lot easier if you have one.
What is a PESEL?
A Pesel is an 11 digit identification number partly based on your date of birth. Polish people are assigned one within a couple of months of being born. When my daughter was born here in Poland we simply called the Urząd Miasta when she was 2 months old and they told us it over the phone. For foreigners you get it in the same place where you do your zameldowanie.
A Pesel is not a VAT number, nor is it a tax number (called a 'NIP' number in Poland), nor is it a national insurance number. It is just an ID number.
How do I get my PESEL?
If you are a foreigner (i.e. you don't have confirmation of Polish citizenship) then a pesel can be applied for when you do a zameldowanie for a a period greater than 3 months. But to register for more than 3 months you will need to have got your karta pobytu already which lets you register for 5 years.
When you do your 5 year zameldowanie make sure you explicitly tell them that you want a Pesel. They are supposed to ask you about it but they didn't ask me at all.
I have heard that sometimes they generate the Pesel automatically and some people didn't even know that one had been generated for them. But for me no-one mentioned anything and on checking today they said I don't have one.
Because the procedure is that a Pesel can only be generated when you register, I therefore needed to de-register and re-register (wymeldować and again zameldować). Unfortunately I didn't have my documents with me so I will come back and do this another time. I was told I would receive my Pesel within 10 days of doing this.
Getting a Pesel is very easy to do and doesn't cost anything. It will save you many arguments in public offices and shops. I wish I had known about this a few months ago...
EDIT - 19th Aug 2008:
I just returned form the Urząd Miasta and was told something different - the regular guy was there and he claimed that he did offer me a Pesel and I declined it. I find that hard to believe (why would I decline a Pesel?) but maybe I misunderstood something. He said that it would now be difficult to issue one. After a few phone calls and playing with his computer he said he would delete me, start over again from new and do it. So in the end it was sorted and I didn't have to de-register and re-register. He said I had to return in a week to collect it. I asked if I could just call by phone and he said no. By this time he was getting grumpy so I didn't try and push my luck any further...