You can delete your own activities. Deleting is a drastic step because it completely removes all information about the activity*. For example, if you delete a forum, all the posts in that forum are lost forever. There is no way to retrieve them.
If you are sure you want to permanently delete an activity, you must first use the Change button to remove all members of that activity. Then click Delete and accept the confirmation prompt. The activity will be removed from your list.
* Technically, information is retained for some time as part of University backups. However we cannot retrieve activities from these backups, which are designed to handle problems like computer failure that affect the entire system. So don't delete anything unless you're absolutely certain you will never want it again!