Whilst it can be possible to recover some files from a broken hard drive, it is a difficult, time consuming, costly process. If only you had another copy of these important files. Perhaps you do, perhaps you are 'savvy' enough to create another copy (not on the same disk I hope!) but on another device; a usb stick, CD-R, an external hard drive or the cloud. If not, let me explain in the following paragraphs what you can do to protect yourself and help you recover from a computer/disk failure.
Right click on the folder or file you want to make a copy of, find the option called Send To... and send it to your plugged in USB stick or CD Writer drive. Easy enough but requires you to find the files that haven't already been backed up first. With the CD option, it can get extra complicated because you have a further step to actually write the files or commit them to the CD - Once written to you can't usually add more files (unless you've enabled multi-session) or remove them.
Install some special backup software, tell it the folders you want to backup, and where to. Let it do the work for you. Some great software for this is GoodSyncToGo (there's a trial version - just Google for it) - when installed on your USB stick or external harddrive it starts automatically (if you desire), and backs up any new files it finds. If you want to buy the software you can do so through All Tech Plus with a modest discount from the RRP, and even have ATP set it up for you and show you how to use it.
Google, Microsoft, DropBox, Apple (iCloud) to name just four companies offer free online storage of a fairly generous capacity. Copy your files here, or even simply use the provided synchronizing software to keep copies duplicated on your laptop with online storage. This means you can access your files from anywhere too! If you have a Google (Android) based phone you can automatically backup your photos to your Google area with unlimited storage. iCloud offer something similar for Apple users.
Don't forget keep your backup safe. Separately from your computer at least to avoid theft. Another building to avoid fire risk.
Where to store your second copiesIf you have a second copy of your important files somewhere then you have implemented a disaster recovery plan. If your computer or its hardware fail, it is a relatively pain free process to copy the data from your second location back onto new equipment. The location of those copies can be in any number of places; some of which are outlined below.
Backing up your files onto CD's (many computers already have cd writers built in) or even DVDs is one option for backup storage. The media (disks) themselves are cheap though their capacities may be limiting requiring the use of more than one, and backup is a slow process. The media is also often write-once only, though depending on how you setup your backup you may be able to add files to the disk until it is full. Backup copies must be stored carefully, in a cool dry environent and not subjected to strong sunlight as these can effect the reliability of the media.
USB sticks represent an alternative, their capacities per device are much better than CDs/DVDs, and of course they're quicker. The highest capacity ones still seem a little expensive but the more common lower capacity ones are cheap. If you're looking to buy one for personal backup purposes, seek something with a minimum of 32Gb of storage. As a side note, many come with file encryption software installed on the device - unless you are good with passwords or if it is super important to keep the backed up data from prying eyes I wouldn't recommend using it, just keep the USB stick safe. Be aware that USB media have a limited amount of write cycles; this probably won't impact on most people providing you aren't constantly writing and deleting from the device on say a daily basis. Just use the media for backup only.
Online storage provided by Google, Microsoft, Apple, Dropbox etc.. - good storage capacity. Slow to transfer files. If the service is offline or your internet connection is not working however you lose access to your backup.
External Hard Drive
These offer much higher storage capacities than the previously mentioned options. They're relatively cheap too. Connect to your laptop regularly, couple it up with some good backup software and you're good to go. This is the best option.