There are no storage formats that don't fail after an extended period of time; the hard drive on your computer will eventually fail. The solution to keep your data from being lost is to create backups.
As a rule of thumb, for anything important, you should have at least 3 backups for anything important, in at least 2 different formats and at least 2 different locations. Backup devices require some financial investment, but you can't buy back the time and effort put into a group project or photos of memories with friends.
U of I Box
U of I provides 50 GB of cloud storage to all faculty, staff, and students through U of I Box. This allows you to store and access files anywhere that you have an Internet connection. For example, if your laptop is stolen or broken, you can still add the finishing touches to your 20-page paper that's due the next day at a lab computer.
External hard drives
An external hard drive is the quickest way to backup or recover data. Many hard drives come with software that help you back up your data with just the press of a button. Windows (File History) and OS X (Time Machine) also have their own built-in applications that can automate backups.
When buying an external hard drive, it's best to select one that can connect not only with your computer, but other computers as well. USB 3.0 connections are generally fast and broadly compatible. Another aspect to consider is storage capacity. More storage costs more money, but you always want to get more storage than you currently need, since the amount of data you have will likely only increase. If you need any assistance with backing up or restoring your data, submit a help request.
You can purchase external hard drives at the Illini Union Tech Zone.