dd1's school also has zero PTA involvement. They have a parent liason person (who is also one of the parent governors) who is lovely, and helps organize various activities.
This weekend, they have asked Reception/Yr 1 parents to come and help dig their allotment (they grow veggies the kids get to cook with!), and make fund-raising chutney in the canteen kitchen.
From what I can gather, activities that help the school and create a sense of community generally are more successful than straight 'come and socialize' type events - the latter probably scare too many people
Plus the Dads get involved in things like gardening/making a slope for the nursery playground etc.
I actually think the best ones at our school are the ones focused more on socialising, with funds a happy by-product. an awful lot of people (me included) find the christmas fair type thing a bit of a pita. there's very little there that I actually want to do/buy but I go, and help out, mostly out of obligation. by far the best things we do are a quiz night - no kids, pizza, beer,a very good quiz and entertaining quiz-master. it's really good fun. and a family barbecue - in the summer, 6-8.30 with a live band. the kids love it and the adults do too. I think they work because they are actually fun. on a smaller scale we have welcome teas at the beginning of term - cup of tea and some cakes at about 3-4. obviously this can;t include everyone but it's a really nice ice-breaker for those who would be picking up anywa, and for some who wouldn;t normally be there at pick up time but make the effort to come for the tea.
We're holding a saturday afternoon family quiz this term. We'll serve coffee, juice and cakes. The idea of it is to get parents chatting, but the quiz will provide a bit of structure and hopefully break the ice.