How can I upgrade pip on Ubuntu 10.04?

Remove your system wide installation of pip:

sudo apt-get purge python-pip

Then install a fresh copy of pip:

curl  https://bootstrap.pypa.io/get-pip.py | sudo python

Tested on ubuntu 10.04 i686

I suggest you to use virtualenv. For further details see the Official pip documentation

As a matter of fact, pip install --upgrade pip does work, but it install a new pip, in my case pip-2.6. So the command to uninstall is pip-2.6 uninstall package-name.

In my case after a sudo pip install --upgrade pip on ubuntu 10.04 /usr/bin/pip is unchanged but /usr/local/bin/pip is pip 1.1

pip --version
pip 0.3.1 from /usr/lib/python2.6/dist-packages (python 2.6)

/usr/local/bin/pip --version
pip 1.1 from /usr/local/lib/python2.6/dist-packages (python 2.6)