What computer architectures are available?

The list is available here: https://wiki.ubuntu.com/SecurityTeam/FAQ#Architectures

Ubuntu's supported architectures change over time, but x86 32-bit ("i386") and x86 64-bit ("amd64") are the most standard architectures, with ARM ("armel") becoming a recent addition.

The linux kernel is ported to several dozen architectures, and many of the basic linux tools are also ported to those architectures (libc, gcc, etc.).

Ubuntu support is primarily focused around i386 and its 64 bit extension, for obvious reasons.

However, according to the ubuntu wiki, there are officialy supported ports for 3 architectures. And 3-4 more that are not officially supported by canonical. However, all 7 architectures are installable from the "Alternative Install CD", even if not all of them are maintained by canonical

The installation guide has documents for all 7 of the supported architectures.