Evernote (for students age 13 and over) allows you to capture ideas – just create a note. Evernote helps you capture anything anywhere and find it again! The search function is excellent. You could just use the web application (the free version gives you everything you need). You can also download a program for Windows (check with your parents before downloading programs); there are also versions for mobile devices. See this link for a short video introduction.
Deadline is a very simple application which lets you store reminders online. You will receive email reminders.
Track Class allows you to keep a calendar of your assignments, take notes and send yourself reminders.
Remember The Milk is an online task manager for students age 13 and over.