While you can use the techniques described in the link provided in csgeek's answer or in this article to pin or hold packages, I still would not recommend that anyone other than a very experienced user do this. The dependency relationships between packages can be complex and are not always obvious.
I am leaving this answer, which suggests removing a package you do not use, in place as a possible alternative which might also be useful in some cases.
But I want to make it clear that removing a package should only be done if you are certain that no other package you do use depends on it!
For example, I use gmail so I have no use for thunderbird. I can (safely, I think) open a terminal window and use
sudo apt-get remove thunderbird
to uninstall thunderbird and avoid downloading and installing updates for it.
But BE CAREFUL. If you remove/uninstall a package which other packages use then you could break your Ubuntu installation. Depending on how badly you break it, you might not be able to easily recover.
If removing a package will result in a large number of additional packages also being removed, I do not think you should do it. In my opinion, you are likely to break something.
I would also suggest that before you remove a package you use the
--assume-no option on
apt-get as, for example,
sudo apt-get -V --assume-no remove thunderbird
This command will run
apt-get but will not perform the remove. However, it will list the actions which would be taken if you did remove the package. This will give you the opportunity to reflect on how much possible damage removing a package might cause.
-V option in the command above just provides more information about the specific version of the packages
apt-get might change.)