Linux is not Windows, you do not need any special apps and whatnot to do a complete system backup. You can do it yourself if you choose.
Do you have a spare harddrive? Can you borrow one for a day or so? Just big enough to take your entire installation as is.
How do I find out how much disk space has been used up?
In a terminal:
df -h
Now you know how much space you need to do a COMPLETE backup.
Install the new backup harddrive, boot the Ubuntu liveCD but do not use the install option, use the "I'm trying this stuff out" option that takes you to a fully functional desktop.
Now in a terminal:
mkdir /mnt/hd1
mkdir /mnt/hd2
mount /dev/[original Ubuntu partition I want to backup] /mnt/hd1
mount /dev/[backup harddrive] /mnt/hd2
cp -r --preserve /mnt/hd1/* /mnt/hd2/*
This will take a while depending on how large your installation was.
Now you have a FULL system backup! I know you do not need to copy /dev /proc /var, but on most modern distros they get flushed with your next boot anyway so no harm done. Just make sure when you do this that those dirs are not in use by the OS otherwise... wait, just try it and after one hour on cp /proc tell me what you learned.
To get your original installation back after the format, just do everything over and copy all the files back.
Reinstall grub:
sudo grub
find /boot/grub/stage1
root (hd0,0) <--If you only use Linux and no Windows
setup (hd0)
quit
And I think you should be done.
I do not know the setup of your system or what you are trying to do, but if you only want to get more space for your Linux install Gparted and grow and shrink the partions as you need.