As usual, you don't know what your users are storing where and how much.
To identify the largest folders or files you can use this small command line:
du -a /var | sort -n -r | head -n 20
This shows you the 20 top files/folders under /var.
Of course you can also run it agains your root folder, it will then take somewhat longer to complete.
For more details look at this post.