Nothing at all for any of my three DC when they were 1yr old! (And not much later on either.)
I think I did 1 or 2 parties for each of them during their primary school years. (Just some school friends over to the house. Very simple.)
It hadn't even occurred to me that ppl might have a party for a 1yr old ... until I was invited to a party for a 1yr old 'friend' of my 1yr old DC1. I didn't know the hostess very well so I wasn't sure what to expect. It was her 1st DC, so I thought she was just being a bit 'precious'!
There was only 1 other guest (Another mum who I didn't know at all. With her 1yr old DC1.). So the 3 of us had a cup of tea and a piece of cake at a table, with our DCs on our laps.
I thought it was OK, but slightly bizarre. (But then we never really did birthday parties when I was growing up!)