If you are building a WordPress website "from the ground up", especially if that WordPress website is for a business, it's worthwhile considering an adaptive/responsive theme, so that you don't have to later develop a mobile version of that website.
Here's an explanation of responsive themes:
The most popular topic of discussion at the moment, amongst web designers anyway, is undoubtedly responsive web design. This is in response to the popularity, over the past couple of years, of visitors opting to use a mobile device of some sort (Android, iPhone, iPad..) to access their favorite web sites.
Just to give you a quick overview, responsive web design allows you to offer a specific and optimised screen size layout that is based on whatever device (mobile, tablet…) the visitor uses.
With responsive layouts in mind, with this post we have taken a look at what responsive themes the WordPress community currently freely offers. You will be surprised at the quality of the themes we have found. And remember, all of these themes are free to download.
Read the full article here: http://speckyboy.com/2011/09/05/15-free-wordpress-themes-with-a-responsive-layout/
If you’re using free themes, here are a few places to find them. You can also search Google for “free WordPress themes” and create your own collection of links to themes for future use.
http://www.woothemes.com/themes/free/
http://slashmarks.com/httpslashmarks-com19-free-photo-gallery-portfolio-wordpress-themes/
http://wordpress.org/extend/themes/
You can sign up for a free account and download free themes (and plug ins) at: http://premium.wpmudev.org/free-wordpress-plugins-and-themes/
http://wordpress.org/extend/themes/
http://wordpresstemplates.name/
http://www.dailyblogtips.com/wordpress-themes
http://www.themelab.com
http://wordpressthemes.name
http://www.freewordpressthemes.com/mostdownloaded/
http://topwpthemes.com/
http://codex.wordpress.org/Using_Themes/Theme_List
If you are allowed to use a paid theme, here are a few great websites to find really good WordPress themes.
http://gorillathemes.com/themes/
http://www.elegantthemes.com/
http://www.woothemes.com/
http://themeforest.net/category/wordpress<
http://www.inkthemes.com/
http://ithemes.com
A framework is useful if you have html/css skills and have the ability to develop custom WordPress websites (including mobile websites). Below are links to a few frameworks.
If none of this makes sense to you, just skip this part and don’t worry about frameworks.
From Wordpress.com : A Theme framework is a Theme designed to be a flexible foundation for quicker WordPress development, usually serving as a robust Parent Theme for Child Themes. Some Theme frameworks can also make theme development more accessible, removing the need for programming or design knowledge with options pages.
http://www.studiopress.com
http://presswork.me/
http://diythemes.com/
http://www.rootstheme.com/ (free)
http://prothemedesign.com/themes/elemental
http://themble.com/bones ( free and has a responsive/adaptive framework which means one theme can work on desktop, tablets and mobile)
A more illustrative explanation of Theme Frameworks
http://www.hyperarts.com/blog/intro-wordpress-theme-frameworks-child-themes/#more-8581