Can a Raspberry Pi run Ubuntu?

Solution 1:

From the Official FAQ Page at Raspberry Pi:

What Linux distros will be supported at launch?

Fedora, Debian and ArchLinux will be supported from the start. We hope to see support from other distros later. (Because of issues with newer releases of Ubuntu and the ARM processor we are using, Ubuntu can’t commit to support Raspberry Pi at the moment.) You will be able to download distro images from us as soon as the Raspberry Pi is released, and we will also be selling pre-loaded SD cards shortly after release.

Source: My answer on Raspberry Pi SE

EDIT

It seems that since the launch of Raspberry Pi 2, Snappy Ubuntu Core can be run on RP2.

Thanks to a very successful collaboration between the Raspberry Pi Foundation and Canonical, the company behind Ubuntu, we are pleased to announce that Snappy Ubuntu Core is available for the Raspberry Pi 2, the latest Raspberry Pi family member.

• Snappy Ubuntu Core on Raspberry Pi 2 | Ubuntu Insights

However, it should be noted for the anxious that this is not a desktop version of Ubuntu.

Solution 2:

Currently not - Canonical only support ARM's ARMv7 processor architecture and the Pi has an ARMv6 chip.