If you are using Ubuntu 12.04 on an older computer with a Semperon CPU, you will soon find that Flash is not working and therefore Youtube videos will not work either.
Adobe Flash built with SSE2 flag
This is because Adobe has build the recent Flash versions with the SSE2 flags enabled, yet many Semperons lack this particular flag.
$ cat /proc/cpuinfo
vendor_id : AuthenticAMD
cpu family : 6
model : 8
model name : AMD Sempron(tm) 2600+
flags : fpu vme de pse tsc msr pae mce cx8 apic mtrr pge mca cmov pat pse36 mmx fxsr sse syscall mp mmxext 3dnowext 3dnow up
GNU Gnash as an alternative
The solution is simple: uninstall the Flash Plugin Installer, and then install the free and open source alternative: Gnash.
Just do these commands from a terminal:
sudo aptitude purge flashplugin-installer sudo aptitude install gnash mozilla-plugin-gnash
Now, log out and login again, and Flash should work.