The Ubuntu family, the most commonly used:
NB: Updated for 16.04 LTS versions! Note the change in minimum required CPU: no longer will a Pentium II (Lubuntu) or III or a AMD K7 (Xubuntu) do, it seems...
Flavor Desktop Unity Gnome KDE Mate Xfce LXDE CPU Req 2 GHz dual core processor
(better recommended), or
ARM Cortex A7
(better recommended)2 GHz Celeron
(better recommended)2 GHz x86
(better recommended)Pentium 4 or
Pentium M or
AMD K8
(Core 2 Duo 1.6 GHz
or better recommended), or
ARM Cortex A7
(better recommended)Pentium 4 or
Pentium M or
AMD K8
(better recommended)Pentium 4 or
Pentium M or
AMD K8
(better recommended)RAM Req x86: 2 GB
(more recommended),
ARM: 1 GB1.5 GB
(more recommended)512 MB
(1 GB or more recommended)x86: 512 MB
(2 GB or more recommended),
ARM: 1 GB512 MB or more
(minimum install can
be done with 128 MB)128-384 MB
(512 MB or more recommended)Disk Space x86: 7-25 GB,
ARM: Less than 16 GB7-16 GB 4-10 GB 8-16 GB,
ARM: Less than 16 GB2-6 GB 384-800 MB
The minimum requirement figures given take into account the install on a 32-bit ('legacy') system.
When you have a 64-bit system you have the advantage of a better CPU than these minimum requirements and almost no limitation in the amount of RAM -the more the better- you can place, other than the limits of your mobo.
Most x86 systems (read x86-64 systems) nowadays can take at least 8 GB of RAM and a speed of 1.5 GHz for a CPU, APU or SOC seems the bare minimum now.
As an example: My 'budget' 2050 MHz Athlon 5350 Socket AM1 Ubuntu and Xubuntu systems are loaded with 16 GB of DDR3 RAM.
You may have some older hardware lying around though....
ARM boards as the Raspberry Pi 2 and 3 are very limited in the expandability of system RAM (as in you just can't do it): when you find out that the 1 GB of the Pi 2 or 3 will not be enough, you should consider e.g. the 2 GB -and 2 MHz- ARM Cortex-A53 equipped Odroid C2.
I am having no trouble running Ubuntu Mate 16.04 on my 2nd Raspi 2 though and I expect an even more pleasant experience running it on the (faster) Raspberry Pi 3.