The OP links to this site: http://builtwithbootstrap.com/ There are definitely a few sites that look barely-out-of-the-cookie-cutter...however, there are others that are only vaguely bootstrappish at a glance. What do people consider the minimum amount of alterations before a bootstrap site looks unique enough? Besides color I mean....font-spacing and sizes? Going from a 12-col grid to 15/16/20-grid?
1- Navbar, the dark gray will not fly, tweak the height of it too or remove it all together.
2- Background of your container, give it some life. Here is a good place to start- http://subtlepatterns.com/
3- Special font for your branding/ H tags, boom (http://www.google.com/webfonts)
4- change up the button colors a tad, if only one, the blue one, it seems to be everywhere.
The above items will take you 15-30 min depending on how many combinations you try out & will take you pretty far.