How to change the default GCC compiler in Ubuntu?

As @Tommy suggested, you should use update-alternatives.
It assigns values to every software of a family, so that it defines the order in which the applications will be called.

It is used to maintain different versions of the same software on a system. In your case, you will be able to use several declinations of gcc, and one will be favoured.

To figure out the current priorities of gcc, type in the command pointed out by @tripleee's comment:

update-alternatives --query gcc

Now, note the priority attributed to gcc-4.4 because you'll need to give a higher one to gcc-3.3.
To set your alternatives, you should have something like this (assuming your gcc installation is located at /usr/bin/gcc-3.3, and gcc-4.4's priority is less than 50):

update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-3.3 50

--edit--

Finally, you can also use the interactive interface of update-alternatives to easily switch between versions. Type update-alternatives --config gcc to be asked to choose the gcc version you want to use among those installed.

--edit 2 --

Now, to fix the CXX environment variable systemwide, you need to put the line indicated by @DipSwitch's in your .bashrc file (this will apply the change only for your user, which is safer in my opinion):

echo 'export CXX=/usr/bin/gcc-3.3' >> ~/.bashrc

Here's a complete example of jHackTheRipper's answer for the TL;DR crowd. :-) In this case, I wanted to run g++-4.5 on an Ubuntu system that defaults to 4.6. As root:

apt-get install g++-4.5
update-alternatives --install /usr/bin/g++ g++ /usr/bin/g++-4.6 100
update-alternatives --install /usr/bin/g++ g++ /usr/bin/g++-4.5 50
update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-4.6 100
update-alternatives --install /usr/bin/gcc gcc /usr/bin/gcc-4.5 50
update-alternatives --install /usr/bin/cpp cpp-bin /usr/bin/cpp-4.6 100
update-alternatives --install /usr/bin/cpp cpp-bin /usr/bin/cpp-4.5 50
update-alternatives --set g++ /usr/bin/g++-4.5
update-alternatives --set gcc /usr/bin/gcc-4.5
update-alternatives --set cpp-bin /usr/bin/cpp-4.5

Here, 4.6 is still the default (aka "auto mode"), but I explicitly switch to 4.5 temporarily (manual mode). To go back to 4.6:

update-alternatives --auto g++
update-alternatives --auto gcc
update-alternatives --auto cpp-bin

(Note the use of cpp-bin instead of just cpp. Ubuntu already has a cpp alternative with a master link of /lib/cpp. Renaming that link would remove the /lib/cpp link, which could break scripts.)