My mum told me the other day that I'm around 1/32nd Irish. Most of her side's been traced back to England; we don't have as much information about my dad's side, but think most of them were a mix of German and English.
Most of what we've traced back is Irish from somewhere outside of Cork for the Dumphys(or 'Dunphy's). The 'other-side' seems to be fairly Scottish (but the same is there isn't much info). But of course that is mixed into mostly Canadian :) AND you can still be Irish for a day *kiss* ;P