A gmail account is incredibly useful when it comes to staying organized. You can use google drive to create folders and word documents for all of your homework. It also allows you to share these documents with other people. You could, technically, add your entire class to a document together and share your class notes. This allows for more comprehensive studying. You can also create powerpoints in google drive. This allows you to access your homework from any location where you have internet access--as well as from any device. The google calendar allows you to keep a calendar of assignments and when they are due/assigned. This could be extremely helpful.
I am an Android user so the apps I recommend may not be available for Windows and Apple users. OneNote is a free notebook/binder that can be organized easily and can be accessed on your phone, computer, or tablet. Astrid is also a free app. It allows you to make lists of what you need to get done, but also lets you create collaborative lists so everyone can see if the task is done (this is great for group projects).
I too am an Android user, so the Marketplace is a little different in terms of applications available. A couple that I use to stay organized with homework and life in general are Google Calender Google Tasks. They are both free and come with an Android phone. However, if you do not have an Android, they are also available for PC use as well.
Another app I like to use is called Asana. This app is an all-in-one to do list, calender, and organizer. It is beautifully colored (is mostly set in soft hues of orange, gray, and other colors) and works exceptionally well.
RescueTime is a great app for your computer (or iPod/iPhone). It links up to the internet and helps you monitor your "digital distractions", which basically means that it can block certain websites, such as YouTube, for a time that you set so you can get work done.
My personal favorite app that doesn't really have to do with homework, but it really helps you get things done, is called CARROT To-Do. CARROT is a little female AI is very snotty and sarcastic, and will get very angry when you are not productive. You earn points for every task you complete and as you level up you unlock things such as your own cat (mine is named Professor Cat haha). It is a very fun app that also forces you to be a productive member of society, which includes getting homework done :)
There are a lot of free apps to choose from to help sort out your school work, so I will name a few with some information about each.
myHomework Student Planner (Avg. Rating 4.3): Nice interface, syncs with myHomework planner account online. There is an ad-free version, but only if you pay for the app. This free version comes with ads, which might get annoying.
Homework Planner by Tom Richardson (Avg. Rating: 3.9): Simple format, no special permissions required to install, but it doesn't look like it has a syncing feature, so anything you record will just be on your phone. It lets you track your grades along with your assignments.
Homework Tracker (Avg. Rating: 3.7): Nice interface, records homework, tests, quizzes, and grades. Has a feature that will save pictures as assignments if a teacher writes an assignment on the board. No syncing.
There is also, as Wiggin42 suggested, Google Calendar, which syncs with several devices and allows for some pretty extensive organization. If you are looking for something really basic that you can have right on your phone, I know some phones have built in planners (per week or per month) that you can set up right on one of your home pages, with an alarm/notification you can set up to remind you when an assignment due date is getting closer. I've been using that one and it has been really helpful.
I'm an android person so I prefer Google Calendar. It readily syncs to both my laptop and phone (and sends reminders to each!). It has a simple interface without any gimmicks or annoying adverts. I can color code tests, quizzes, projects, and finals. I can keep my extracurricular activities, school stuff, and scholarship deadlines all on separate calendars for easy viewing.
There are many apps on the appmarket that can really help you. My personal favorite is iHomework because there are calenders and it divides your work among class subjects. It also sync across different devices and can be downloaded on iTunes. If you do not want to pay, there are many free apps out there. A good app for notes is Evernote, because you can access it on any computer and phone and it is free!
One of the best app that helps me organize school works are OneNote. On this OneNote I can take notes and put file. OneNote is like a binder. Its easier and u won't have to carry lot of pages.