I wholeheartedly agree with every post so far. With a band like the Breakfast who jams and improvises, you are going to get a whole slew of different answers and that is the beautiful part of all this discussion. You really can't go wrong.
As far as shows you must hear, the year 2001 immediately comes to mind. I don't know what it is about this year. Maybe its the abundance of crystal clear audience/sbd matrix recordings and the crazy, diverse setlists. Add to that the exuberance of youth and being a part of something that has some real energy and momentum and potential and power! Got damn they do some sweet, sweet jamming. Some notables:
5-5-01, Baker Quad, UMASS. Excellent show all around. 7-26/27-01, Holyoke and then Camp Creek. The band is riding high on a crest with a whole summer full of awesome shows. 12-7-01, Danbury, CT. A show short on songs and long on jams. What more can you ask for? Epic performances all.
But there are great shows in every single year that this band has existed. Seriously. Sample different years and you will hear different sounds because of different lineups and just by the nature of playing experimental music.
Yet I digress. Some more great shows to check out:
4-5-02 Powder Hollow Barn. Great show and just looking at the setlist gets me a little excited. 6-15-03. Family Jam. Just listen. 6-29-03 Jellyphish Lounge Houston, TX. A very unique sounding show. A different spin on your daily Breakfast. Someday I will mess around with the files that are on the archive and boost the levels.
Turkey Tour November 2004 are all solid shows. 8-7-05 Family Jam. Definitely check the new multitrack version on the archive.
I love the west coast tour in March of 2006. Very nice run of shows in September of 2007 with then-new keys player Matty O. 11-28/29-08 the return of the Branch are must hear!
I will post more as I think about this. Go and explore the archive. I'm sorry I didn't link each show but I'm hoping it will be fun for you to go and look around at setlists and sample some shows.
http://archive.org/details/PsychedelicBreakfasthttp://archive.org/details/TheBreakfast