Olá,
De acordo com o próprio site do Ubuntu, segue as especificações mínimas, óbvio que com algumas personalizações podemos diminuir ou aumentar tais requisitos.
System Requirements (Desktop Edition)
Ubuntu is available for PC, 64-Bit and Mac architectures. At least 256 MB of RAM is required to run the desktop install CD. Install requires at least 4 GB of disk space.
Ubuntu Server Edition is meant to run on any Intel or AMD x86, AMD_64, EM_64T processors as well as Sun Sparc T1 processors. It requires a minimum of 128Mb of RAM and 1Gb of disk space.
Para maiores detalhes acesse:
www.ubuntu.com