Image File Size –
If you are uploading your own images to your website’s hosting server you should take note of the file size before you upload.
Images taken directly from a camera will have a large file size (4MB or higher) but images can be displayed on websites at a much smaller resolution without any noticeable change in quality.
There are many desktop applications and software available to resize your images  – the best method is to upload your images at the exact dimensions required by your website.
Generally images can be as small as 45kb (100 times smaller than original) and still look great on line.
Image Duplicates
Even though Content Management Systems such as Worpress and Joomla will automatically resize your uploaded images for you, they will still keep original image stored on the server.
Depending on how your website is configured it many producing many unnecessary duplicates at different sizes. Speak to your developer or refer to the documentation for your system.
Video Hosting
Streaming video can take up a lot of space – consider using Youtube or Vimeo and embedding videos into site instead of storing them all on your own server.
Offsite Storage (Content Delivery Networks)
In some cases, if you have a lot of media files stored on your site (even if you reduce all of the file sizes – see above), they can take up a lot of server storage. In this situation there can be advantages to using a Content Delivery Network to store your media files in basic but very cheap storage service – speak to your developer about this solution.
Email Storage
If your hosting service includes email storage check the settings. If all of your emails are being left on the server they will become costly. Using a desktop application (iMail, Thunderbird, Live Mail) to download, view and organise your email – make sure the setting “delete emails from the server once downloaded” or similar is selected.