Ubuntu x86 vs. Ubuntu AMD64
Ubuntu is currently among the most popular of all GNU/Linux distributions. Since the release the AMD64 architecture, many Linux users have debated whether or not it is worth going to a 64-bit version of their operating system if they have a capable processor. Although almost all newly purchased computer systems are capable of doing so, most people continue to use the 32-bit version of Ubuntu.
The ability to address over 4GB of memory is one of the few advantages with the AMD64 architecture which would affect desktop users. However, recent versions of the x86 Linux kernel have the ability to address arbitrary amounts of memory, with little or no performance hit.
Encryption and decryption using large keys also shows significant performance improvement, so if a user has an encrypted hard drive or frequently uses encrypted connections, there may be a noticeable improvement in performance. However since most applications are not yet optimized for this architecture, there may be no performance increase, or even some slowdown with everyday applications.
The ability to perform 64-bit mathematical operations can speed up scientific applications enormously.
A hot topic that receives very little attention is that of application support on AMD64. A comprehensive list of compatibility problems has not been published by Ubuntu or by its user community, and issues pertaining to the 64 bit version are generally handled on a needs basis.
Although this fact is hardly surprising. GNU/Linux distributions are very, very complicated, consisting often of over a thousand separate programs which together make up a working system. Most of these programs are invisible to the end user, and each of them may be developed and maintained by a different developer community, who have their own methods of testing, fixing and redistributing their software. This makes diagnosing stability problems and incompatibilities in the system as a whole a skilled task, requiring not only an understanding of software and computers, but an understanding of the GNU/Linux system as a whole, and how each program acts and interacts within it.
The distribution has significant stability issues, including but not limited to a large number of desktop applications. However the isolation of a problem such as an intermittent crash in something as complex as a Linux system can take time, and many similar problems may in fact share a single common cause, such as a broken software library that all affected applications depend on.
It is important to remember that the vast majority of the AMD64 distribution is fully functional, and very stable. GNU/Linux has been running successfully on many different platforms for as long as it has been around. As more people use this version, it will receive increasing developer attention.
Ubuntu's 64 Bit Philosophy
Since 64 bit Linux kernels fully supports 32-bit applications, it is technically possible to revert to a 32-bit version of any application.
On philosophical grounds, Ubuntu insists on releasing a pure 64 bit distribution. This means that the user can't directly install any 32 bit applications through its built-in package manager unless no 64 bit versions are available. (See Synaptic or apt)
Some users complain that Ubuntu should slowly phase in 64 bit computing, from the kernel up, using only 64 bit programs that are presently functioning at par with their 32 bit counterparts. Since the majority of 64 bit applications already work fine, only a few programs would be affected by this change. Although it should enable a user to upgrade to the 64 bit version of Ubuntu with no issues whatsoever.
Probably the most common use of a desktop computer is the internet. That is why it's absolutely essential that any desktop distribution have a working web browser. As said before, in most cases on Linux we have the option of falling back on 32 bit applications, since the kernel supports them, and the libraries are kept separate. However Ubuntu is unlikely to support this, and that leaves it up to the user to come up with solutions to programs that just don't work.
In the case of 64 bit Firefox, it works reasonably well on Ubuntu AMD64 as of 7.10, although it is noticeably less stable on some systems. There is also noticeable slowdown from what one would be used to on a standard 32 bit browser, but this can be expected since the architecture is relatively new and untested.
Its plug in wrappers (programs that help Firefox talk to plug ins) are also 64 bit which limits the browser's plug in support to only those which have been successfully ported. Many companies have been reluctant to port their proprietary software to 64 bit Linux as at the moment, as it is a niche within a niche. However Adobe provide a prerelease 64 bit version of Flash Player. 
Confusingly however, the Ubuntu package manager includes the 32 bit version of Adobe Flash and lets the user install it, only to discover that it doesn't work. It is possible to replace the plug in wrapper with a 32 bit one, but this solution is not officially supported by Ubuntu and can damage the installation.
The best solution would obviously be to force the user to use the 32-bit browser if they want flash functionality, by treating it is a dependency.