I was in a very similar situation a couple years back when I decided to go into the Peace Corps. I ended up doing strictly a '2 weeks notice' type deal. My reasoning:
-I worked for a small-er company that had somewhat of a mixed history regarding letting people set their last days vs well if you don't want to work here anymore get lost. I ended up working the full 2 weeks. But if there's any doubt you could be compromised financially, I wouldn't say so until you're 100% comfortable being unemployed in the very near future. If you work for a large company you certainly aren't the first person to leave for grad school, try to find out your company's track record regarding this.
-I wasn't absolutely 100% I was going until a month before anyway. The 'lead up' things you do for PC are different for B school but I definitely wouldn't commit to quitting before say your school has run its background check / you've got your financing squared away to name a few.
-I also wanted to do some travel beforehand, and definitely recommend doing so for those whom this will be their first real 'gap' between jobs / education.
Last perhaps insignificant note: Most company benefits like medical, dental etc kick in for the month on the 1st. So if you work your last day on say June 1 instead of May 31, that's a whole other month you are covered. Obviously I gather most people here are very young/healthy but thought I'd mention it.