I don't really have a favorite. I tend to not like to do the same thing twice, so the only one I've make more than once is the Chinese Coin. Start with just squares then work your way up to triangles.

My all time favorite block is the New York Beauty, this is not a beginner block.

My favorite beginner block is twisted sister, there is a tut on it in the tutorial section, it is very easy, goes together really fast, and looks good. Don't have any pictures of it, but I have made about 17 double bed size quilts with my mom and sister to give to all my nieces and nephews. They turned out great and we got them all done in a short time.

Anything log cabin...can be beginner to advanced... so many options, so many ways to lay out the basic blocks... so easy to do with strip piecing... but then you can go pretty advanced with the log cabin by getting into curvy ones, etc. I have done many and always go back for more...

Turning Twenty - easy

Yellow Brick Road - easy

Log Cabin - Easy

Now I've given this some real thought and I've got to say that I love the Carrie Nation block. There's also one that I adapted from a counted cross stitch pattern that was called Cherokee Arrow that I really like. I used both in my CW quilt.
http://www.quiltingboard.com/t-39959-1.htm
The Cherokee Arrow is the middle left of the top pix and the Carrie Nation is the middle right.

For me, it's 'the next one'. :-D I don't use commercial patterns and I absolutely love the design process, so my favorite pattern is the next one. That doesn't help you much though does it. :?

One of my favorite patterns is called Fabric Fling