Do we do Pidyon HaBen - Redemption of the first born?

Not usually: Let me first give the background (with thanks to help from Torah and Wiki!).

In Exodus 13:2 at the end of Parshat Bo, God is reported to instruct that: ‘Every firstborn that opens the womb amongst the Israelites, whether human or animal, is to be set aside as holy to Me, for they are Mine.’

Moses seems to expand on this in Exodus 13:12-13, explaining that firstborn cattle were to be offered as sacrifices, a firstborn ass (not kosher as a sacrifice) was to be swapped ('redeemed') with a sheep (or be 'given' by breaking its neck), and firstborn sons were also 'redeemed', though here it doesn't specify how. Moses' explanation (Exodus 13:15) is that God slew every firstborn in Egypt, animal and human (so this is apparently a perpetual reminder of the tenth plague).

In Numbers 3:41-45, after the sin of the Golden Calf, we find repeated twice the instruction: 'Take the Levites instead of all the firstborn among the children of Israel, and the Levites shall be Mine - I am the Eternal One.'  This is because the Levites were loyal to God, and seems to imply that the firstborn were to be God's functionaries in running the Tabernacle, but lost that honour because of their involvement in the Golden Calf, to be replaced by the Levites. 

There were apparently 273 more firstborn Israelites than Levites, and Aaron and his sons, the priests, were to be given five shekels per head in compensation for each of these, this being called 'redemption money', Numbers 3:46-51.

So we can deduce that originally, the first born son in each family was to serve God as a functionary, but they were replaced by the Levites, and the value of this 'redemption' from a life of holy service was 5 shekels each.

Over the generations and especially in transition from 'Israelitism' (biblical Judaism) to Judaism (Rabbinic Judaism), these details were formalised. The Shulkhan Arukh states that when a Jewish woman gives birth to a firstborn male (but only by natural means) then the child must be "redeemed". The process is that the father of the child purchases back the child from a known Kohen (representing the original Temple priesthood), for the sum of five silver Shekels, or equivalent in their country's currency. The procedure does not apply when the father is a Kohen or Levite (because then the child will continue that line and need not - and cannot - be redeemed from the responsibility).

This redemption ceremony is performed when at least thirty days have passed since the child's birth, since child mortality was common and a child was not considered to have proven its viability until after 30 days.

Pidyon HaBen is an interesting question as we don't usually do it in the Progressive Movement, I think largely because of course we don't recognise Priests etc. and therefore the concept of the firstborn serving as priests... and needing to be redeemed.  (There is also a problem of discrimination - it only counts if your first born is a boy, and if he is not born by Caesarean). But we could adapt and reinterpret the tradition to the idea of thanking God for the start of the next generation, which is a lovely idea, and where it is done, the money is directed to charity - so perhaps it should go to a baby care or mothers' support charity.  On the other hand, there are so many costs involved with a first new baby - and if it is a boy you already have to pay the mohel, so perhaps we don't need another way to make a 'religious charge' on the family!   

Rabbi Jonathan