Project managers and team leads tend to get excited by the idea of using the tasks and issues lists for assigning tasks to members of their team and tracking them in SharePoint. When properly understood, these lists can be helpful, but a couple points should be made first. Although tasks lists can be used to assign tasks to specific individuals, those individuals are not alerted unless they have alerts set up within the list or are actively keeping an eye on the tasks assigned to them when they are using an Office 2003 application that has the Shared Workspace task pane in it, paying attention to the Tasks tab in particular. There also isn't a way "out of the box" to link SharePoint tasks to Outlook tasks, which is a commonly asked question.
Overuse of task lists can result in extra work for the user trying to keep up with his or her different tasks. For example, if Susan works with six different departments and is assigned tasks within those six different departments, she will need to visit six different sites on a regular basis to see what tasks she has been assigned. Susan can set alerts within each task list so that she is informed of changes, but this could result in alerts about changes to tasks that she doesn't care about because they aren't assigned to her. She could set alerts on individual tasks to send her an email when those tasks change, but they won't alert her if a new item is added.
Third-party companies offer "roll-up" Web Parts that will find all the tasks from a range of sites and roll them up to a central location and organize them by the person they are assigned to. This can be a good solution for organizations that really want to maximize the use of SharePoint for project management. CorasWorks (www.corasworks.com) is one such company that offers roll-up Web Parts, including "Task Roll-up" and "Calendar Roll-up."