There is no rule, as far as I know, that says that all yarn bags must look like something that your Great Aunt Harriet or that scary old lady in the Wizard of Oz would make, but that seems to be the prevailing idea. The upside is that yarn bags are so old fashioned and usable that they never really go out of style.
I think that we are on the verge of a great Yarn Bag Renaissance- at least I hope so. After all, there is an enormous amount of fabulous yarn around these days, we need a few good yarn bags to carry it.
I will modestly confess that I have a pattern for a truly marvelous yarn bag in my book Pin Loom Weaving, now available for purchase. Pictures of all the Pin Loom Weaving items can be found under the page heading, Pin Loom Weaving; The Book.
Here are some other great yarn bags including this vintage bag highlighted on Eloomination. You can find the pattern for this classic bag at the Eloomination site: http://www.eloomanation.com/gallery/vintage.php
This next bag is crochet but wouldn't it would look great woven with a pin loom? The pattern is available at: http://archive.berroco.com/exclusives/bramble_bag/bramble_bag_lg.html
My first yarn bag was the product of falling out of love with an earlier project and having a bunch of weavies already made into right triangles. This bag strikes me as the epitome of ugly but useful. It is nice and heavy and will handle all sorts of weaving items. See a simple pattern below. I left out the part about turning the weavies into triangular pieces first, that seems a lot of work for no purpose, but I have posted notes on how to make dual colored weavies to recreate that effect.