I modified LSW's list for Web Programmer, since his list is outdated:
Core Knowledge:
HTML (HTML 4.2 and HTML5)
JavaScript (note: much more than a scripting language)
CSS (CSS2 and CSS3)
PHP5
WordPress
SQL -- MySQL is fine
basic relational database knowledge
Good to Know:
Photoshop
jQuery
JSON
Java
C# on .Net framework
Microsoft Word, PowerPoint, EXCEL, Access, Publisher
Can be helpful on your resume:
Ruby on Rails
Python
Dreamweaver (hand coding is easier and creates better code, though)
Facebook -- creating Fan pages
Mobile web site creation
Creating Apps
Using Social Media and tying into web and mobile sites
Basic internet marketing (branding, driving traffic, engaging customers)
Creating Q-codes and using on websites
SMS -- text messaging service set-up (Twilio)and phone/web/mobile use
Creating and using RSS feeds
SharePoint or GoogleDocs -- way to share documentations with others
Not Sure, I Think Outdated:
AJAX
Perl (clunky language)
Don't bother:
ASP (Active Server Pages)
XML, XHTML -- replaced by HTML5
Another Flash related, such as Action Script and Flash Builder
VBScript -- even IE now uses JavaScript
Drupal -- Use WordPress instead
Eh!
Visual Basic -- If learning either C# on .NET or Java is too hard, then learn Visual Basic on .NET as a stepping stone
Excellent English speaking, reading, and writing skills are golden.
If you know a foreign language, that can help land a web developer job.
People skills (plays nice with others) and soft skills (attention to detail, for example) are also important.