Tasks do not usually 'expire' - even when you pass their due date, although they may not appear if you have a view that excludes them.
If you are running MOSS rather than WSS, you can configure the Information Management Policy (List Settings, Permissions and Management) to set criteria here for removal of tasks. If you did not setup the task list, it would be worth checking here if you are concerned.
You can add workflow via SharePoint Designer to notify you of tasks that are about to pass their due date, likewise if you could create a workflow here for WSS to delete them by certain criteria.
Hope that helps
Rebecca Handley