if your partions are layed out on the harddrive as follows:
/boot(primary), swap(primary), /(primary), /usr(logical), /var(logical)
Then you will have to reformat and back up data. EDIT: back up data, then reformat
You 'could' do this using a boot/tools disk and only backing up /usr to restore after the resize. BUT you have to recreate the / partition in EXACTLY the same starting cylinder. AND /var has to be in EXACTLY the same starting cylinder. and if you do one false move you loose /, /var, /usr. It's not too horribly complicated, you just have to know what you are doing.
I would suggest you back up all important data (most likely it is the /home directory) and place it onto it's own partition. If you have been using your system a while, at least you know the approximate sizes all the partitions need to be and can optimize their sizes.
/ 60g - important data to be moved = (on my system 1g) make it 5 gigs if you are paranoid of something unintentionally increasing its size.
/tmp - you really should think about moving this to its own partition. your results may vary. Mine it 5gig because I compile a lot of packages.
/opt - this may be empty or several gigs. separate, symlink, or add to the size of /
/var - 500mb looks like it will be enough. Unless you have a web server and want all data on that partition.
/usr - 5gigs looks like it will be enough but should be large enough for all the programs you want to install. 76
/boot - fedora defaults to 100mb. I've never used more than this for /boot. and if you don't concern your self with more than 5 kernels, you shouldn't either.
/home now has an awesome 180 gigs!... if that's the culprit anyway.