I really like AsideShop because it’s so foundational, ie. like RSS is foundational; simple but capable of many things; adaptable.
For example, aside from normal posts, I want an online scrapbook, which means I want Tumblr styling. Quotes are the best example, and the first thing I used AsideShop for. I tried several WP Tumblelog plugins, first, but they didn’t do what I wanted and seemed impossible to restyle; they made it easy for beginners, but difficult if you knew a bit of code. AsideShop makes it easy if you know a bit of code.
One idea I might raise is exploring some method of sharing templates. Sharing templates is probably limited by inline CSS, but it makes life simpler for beginners, and those that know a little code can move the CSS to their stylesheets. That’s one option.
Since it seems so foundational, I’m very curious what other purposes people have put AsideShop to. I stumbled across AsideShop looking for a way to split my posts so one topic ran down one column on the main page, and the off-topic, scrapbook posts ran down another column. I’ve found sideblog plugins, but they assume too much and are too difficult to mod.