I'm a programmer and would like to support the development of Bitcoin, but I don't have an original idea for a new project. Where can I find information about tasks and issues that I could put some effort into?
Gavin Andresen, the Bitcoin client technical lead, has expressed a desire that effort be focused on closing bug reports in the client. You can find the current list of open issues on GitHub. You can also find some documentation about how to create your own fork of the project source and how to suggest that changes from your fork be pulled (imported) into the main release in Gavin's post here.