Quick update: the packages available in the repository used by the Intel Linux Graphics Drivers Installer seem to have been fixed for 64bit.
About a month ago, Intel released a tool that allows Linux users to easily upgrade to the latest Intel graphics drivers. The tool comes with a repository used for the driver updates and it's available for Ubuntu (12.10 and 12.04) and Fedora (17 and 18). The repository had some multi-arch issues on Ubuntu 64bit, but they seem to have been fixed, at least according to my test.
I've tested the drivers on my laptop, under Ubuntu 12.10 64bit which previously had some multi-arch issues (which some of you have encountered as well), and the bug seems to have been fixed. I've also tested the repository in VirtualBox, under Ubuntu 12.04 64bit, however since I couldn't reproduce the multi-arch issue in 12.04 before, I'm not sure if it was fixed for Ubuntu 12.04, so use this with care and check to see if it's trying to remove any packages when upgrading. Since I can only test it on one real machine, make sure you know what you're doing when using this tool.
The Intel Linux Graphics Drivers Installer uses a repository so after installing the package, you can use apt-get, the Ubuntu Software Updater or Synaptic Package Manager to upgrade the drivers, which you might find more reliable for now, instead of the actual Intel Installer, (e.g.: so you can make sure the multi-arch bug has been fixed and no packages are removed when upgrading the drivers).
Ubuntu 13.04 already has the latest drivers so there's no need for this tool / repository for now.
The installer doesn't work on Ubuntu-based Linux distributions such as Linux Mint or elementary OS, but you can still use it on such Linux distributions - see: How To Use The Intel Linux Graphics Drivers Repository In Ubuntu-Based Linux Distributions (Linux Mint, Etc.)
Note: Intel Linux Graphics Installer doesn't automatically add the repository key but there are instructions on how to add it under Ubuntu and Fedora on the downloads page.