Page Scraper - Create an application which connects to a site and pulls out all links, or images, and saves them to a list. Optional: Organize the indexed content and don’t allow duplicates. Have it put the results into an easily searchable index file.
Web Browser with Tabs - Create a small web browser that allows you to navigate the web and contains tabs which can be used to navigate to multiple web pages at once. For simplicity don’t worry about executing Javascript or other client side code.
Online White Board - Create an application which allows you to draw pictures, write notes and use various colors to flesh out ideas for projects. Optional: Add feature to invite friends to collaborate on a white board online.
Get Atomic Time from Internet Clock - This program will get the true atomic time from an atomic time clock on the Internet. Use any one of the atomic clocks returned by a simple Google search.
Fetch Current Weather - Get the current weather for a given zip/postal code. Optional: Try locating the user automatically.
Scheduled Auto Login and Action - Make an application which logs into a given site on a schedule and invokes a certain action and then logs out. This can be useful for checking web mail, posting regular content, or getting info for other applications and saving it to your computer.
E-Card Generator - Make a site that allows people to generate their own little e-cards and send them to other people. Do not use Flash. Use a picture library and perhaps insightful mottos or quotes.
Content Management System - Create a content management system (CMS) like Joomla, Drupal, PHP Nuke etc. Start small. Optional: Allow for the addition of modules/addons.
Web Board (Forum) - Create a forum for you and your buddies to post, administer and share thoughts and ideas.
CAPTCHA Maker - Ever see those images with letters a numbers when you signup for a service and then asks you to enter what you see? It keeps web bots from automatically signing up and spamming. Try creating one yourself for online forms.