Web Part Basics

Out of the Box

Great list from Laura (sp2013 / o365)
http://www.wonderlaura.com/Lists/Posts/Post.aspx?ID=214

Overview of Foundation Web Parts - http://office.microsoft.com/en-us/sharepoint-foundation-help/overview-of-web-parts-available-in-sharepoint-foundation-2010-HA101806662.aspx?CTT=1

Outlook Web Part - http://office.microsoft.com/en-us/sharepoint-foundation-help/working-with-outlook-web-access-web-parts-HA101810215.aspx?CTT=1

Chart Web Part - http://office.microsoft.com/en-us/sharepoint-server-help/introduction-to-the-chart-web-part-HA101889216.aspx?CTT=1

Content Editor Web Part- http://office.microsoft.com/en-us/sharepoint-foundation-help/using-the-content-editor-web-part-HA101794745.aspx?CTT=1

Web Part Advanced

Deploy Custom Web Parts - http://technet.microsoft.com/en-us/library/cc261736.aspx

http://code.msdn.microsoft.com/office/SharePoint-2010-Creating-48106cc2

Vendors

SP2010 Web Part Guide from FBWeb - 2010
http://www.fpweb.net/support/resources/free-web-parts/

5 Free SharePoint Web Parts You’ll Love - 2013
http://www.xelleration.com/Blogs/Lists/Posts/Post.aspx?ID=14

SharePoint Intranet Web Parts Series – 2010/2013
http://www.ashokraja.me/post/SharePoint-Intranet-Web-Parts-Series.aspx