I've been cutting paper snowflakes for about as long as I can remember. I remember when I was about six, and I was so disappointed that mine didn't come out as pretty as the ones my dad made. So he taught me a few tricks. Every Thanksgiving weekend, we all grab a ream of paper, some wastebaskets and scissors and go to town cutting snowflakes to decorate with.
One of the biggest factors in how a snowflake turns out is the way it's folded. Many people use a four-pointed fold, which leaves you with a squareish result, like this: