While most WebDrawer implementations are internal there are a few exposed to the public, the ones below are all customised to some extent usually to provide custom branding/layout and targeted searching.
Sunshine Coast council use WebDrawer to deliver property related documents from Content Manager direct to the public. This replaces a four hour process to publish each document with a simple status change on a Record.
Another customer who has customised a WebDrawer instance to provide public access to a sub set of their records is the city of Grand Junction Colorado. A good example of taking the default templates, removing the unnecessary bits and adding your own branding.
I love to see examples of customised WebDrawer and I have seen a couple recently, the first of which is a simple and effective policy portal from Edit Cowan University.
Brian from The City of Portland showed me around their public WebDrawer the other day, if you are interested in customising WebDrawer this might give you some ideas.