I have an old Compaq nx7000 work laptop that I have Ubuntu on.

Just ran:

sudo do-release-upgrade -d
# It's before the official release date of Ubuntu 10.04 so I ran with the -d switch
#  -d, --devel-release   Check if upgrading to the latest devel release is
#                        possible

and got a complaint back that I didn't have enough disk space. I had 1.4GB free on the root (/) partition and it needed 2.2GB to do the upgrade.

Tried the usual process of removing old packages & cleaning up:

sudo apt-get clean
sudo apt-get autoclean

I even ran the System ==> Administration ==> Computer Janitor utility however these steps didn't claw enough space back.

Analysing my space available using df showed that I didn't have enough spare space on my root partition but /home had plenty of spare space

 df -h
Filesystem            Size Used Avail Use% Mounted on
/dev/sda2             5.5G  3.9G  1.4G  75% /
none                  371M  280K  371M   1% /dev
none                  375M  192K  375M   1% /dev/shm
none                  375M  196K  375M   1% /var/run
none                  375M     0  375M   0% /var/lock
none                  375M     0  375M   0% /lib/init/rw
/dev/sda6              22G  4.5G   16G  22% /home

The work around:
I went into /usr and had a look at the space being taken up by the /usr/* directories and discovered that /usr/share was a good candidate for moving to another volume.

# go into /usr
cd /usr/

# preface these commands with sudo
# check the disk usage
du -sh ./*
207M	./bin
2.0M	./games
26M	./include
1.3G	./lib
92K	./lib64
3.8M	./local
21M	./sbin
1.9G	./share
28K	./shareFeisty
238M	./src

# identify that /usr/share is a good candidate to move to another partition with more space on it

# copy it
# -a preserves the permissions and ownership
# -r copy's subdirectories
# -v just shows you what files cp is currently copying
cp -arv /usr/share /home

# mv the old /usr/share and then link it to the new location
mv /usr/share /usr/share.old
ln -sf /home/share /usr/share

# oh and you need to remove the share.old 
# directory to actually get the diskspace back
rm -rf /usr/share.old

# run the upgrade

After the upgrade:
The only problem with leaving the system this way is that some of the links in /usr/share point to relative paths so may get confused. I noticed this because my firefox desktop icon broke.

So I reverted back to the original layout after the upgrade completed:
Reverting back to the default /usr/share configuration

sudo apt-get clean
sudo apt-get autoclean

# make sure you check that you have enough
# space to revert!
sudo df -h
sudo du -sh /home/share

# when you now it's all ok do the following
cd /usr

# when you remove the share link you will lose your desktop icons because they can't find /usr/share/*
# The network manager applet will also quite
# complaining "could not find some of it's required resources"
sudo rm share

sudo cp -arv /home/share ./
# after you finish the cp command reboot to make sure it's alright.