It's been a long time since I've made a paper snowflake. My first attempts were round instead of six-sided. But I soon got the hang of it, thanks in part to Make-a-Flake. Make-a-Flake shows you how to fold your paper into the right shape to make a six-sided snowflake, and then allows you to make practice cuts online. You can undo and redo your cuts until you get the shape you like, and you can post your finished flake in the online gallery. My younger son and I worked together to make the one shown above.
Zefrank.com has a different take on creating online snowflakes. When you visit Zefrank's Create Your Own Snowflakes, you can layer simple shapes and rotate them in 2 or 3 dimensions to create a snowflake effect.
We've come a long way since scissors and paper, but there's still nothing like cutting out your own paper snowflakes and hanging them in the window. If you're looking for inspiration, check out the wonderful collection of Wilson Bentley's snowflake photography in NOAA's Photo Library (search for "snowflake"). These photographs were taken by Wilson in 1902 in Jericho, Vermont.
P.S. [UPDATE:1/9/09] Thanks to a tip from Andy's Parties, I found another on-line snowflake making site,
Rooney Design's Snowflake Factory. Very fun!