One site that was recommended to me is Trello. It's a very flexible project management/to-do/brainstorming tool. It's organized as a number of boards, each of which has one or more lists or cards. You can move these cards between lists and between boards.

The general workflow I've established is to create a board for each project I'm working on, and have three lists: to-do, doing, and done. As you might suspect, cards start out in the "to-do" list, move to the "doing" list when I start on them and go to the "done" list when I finish. However, the tool, as such, does not force you into any particular workflow. That's an important consideration for me, because I've abandoned other task management software when its theoretical workflow model failed to match my real world needs. Trello is flexible enough to allow me to easily construct my own "pipeline" for tasks, with as many or as few steps as necessary, and have different pipelines for different projects.

Trello is a hosted application. However, they have a fairly easy-to-use export function that exports your boards and cards to a JSON document, so you're free to walk away with your data at any time. They also have an API, which you can use to further automate your task management.