To-do and task management
The iPad's Calendar app doesn't include a to-do capability, unlike many computer calendar applications. Fortunately there are dozens of to-do list managers available for the iPad. Three to consider are Appigo's $5 Todo, Alifsoft's $2 Task Pro, and the $4 Toodledo.
Beyond simple task management is project management, which requires a much more sophisticated approach to task and schedule management. One app to consider on the iPhone for such work is the $20 OmniFocus from the Omni Group. It syncs with the desktop (Mac-only) version of the software and ensures the Calendar app has your due dates added. It even can show nearby task locations on a map, in case you're running errands or scouting film locations. Another well-regarded task manager is Cultured Code's $10 Things, which boasts a clean but capable user interface and "smart" today list and scheduling features.
For more personal management tool, take a look at FileMaker's $5 Bento app, which is a lightweight database perfect for tracking records, contacts, to-dos, and other personal tasks and data.
For more work-oriented databases, an app worth considering is DDH Software's $10 HanDBase Database Manager.
The $20 FileMaker Go lets your iPhone access and control FileMaker databases running on a FileMaker server.
Access your SQL database, run queries, and manage records from your iPhone using the $2 SQLTouch.
Mind-mapping and whiteboarding
If you do mind-mapping -- a method of organizing thoughts and items by their relationships -- CMS's $8 iThoughts could be the tool for you. It works with several mind-map formats and lets you export your mind maps to PNG and PDF formats. It also syncs to the Box.net and Dropbox cloud storage services.
Markus Müller's $6 MindNode is another mind-mapping tool to consider. It has a full-screen mode available in landscape view.
If you're looking for a tool to do either mind-mapping or traditional whiteboarding, Pixelglow Software's $10 Instaviz is a strong option.
For more free-form whiteboard sketching, give Y Lau's $1 Pocket Whiteboard a look. The simple app lets you sketch out drawings, formulas, and the like using your fingertip.
You can join a conference held over the Web by using an app for one of the major Web conferencing services. There are free apps for Cisco's WebEx and Callwave's Fuze Meeting Web-conferencing services. Of course, you need accounts on those services to host the meetings from a computer (you can't host them from an iPhone) and attend the meetings. Note that neither service lets you use the iPhone's camera for videoconferencing.