Starship Asterisk*

Do all galaxy spiral arms flow counter clockwise toward the center?

Good question, but no. Here are some links that describe some recent findings in this, um, direction:
http://en.wikipedia.org/wiki/NGC_4622
http://astronomy.com/asy/default.aspx?c=a&id=6478

No.

Imagine a galaxy that has a spiral-in-to-the-left kind of look. Now flip that galaxy over (carefully!). Now it looks like it's sprialling in to the right. And when you figure that the way galaxies appear to us is entirely random, you have to conclude that there is no set pattern to such spirals.

Rob

Oops! RJN got there first.

Here's a previous discussion on the topic: Spiral Galaxies.