After following a subset of this advice, this is how I got the Python GDAL 1.11.0 (the solution should be version-independent, see below) install to work on Ubuntu 14.04 with pip:
Install dependencies:
sudo apt-get install libgdal-dev libgdal1h
pip install by passing along the include path (prefix with sudo for system-wide install) and instructing pip to install the version matching the system installed GDAL version:
pip install --global-option=build_ext --global-option="-I/usr/include/gdal" GDAL==`gdal-config --version`
