I am aplying from the US, i am graduating with my M.Eng this year so still on campus.
among the list were the usual McK, Bain, BCG, Monitor, AT Kearney.
In addition to that i submitted to Mitchell Madison, parthenon, katzenbach, simon kucher, stroud ( a small operations firm here), opera (another spin off from the MMG people), marakon, digitas (interactive agency) and a few others i might not remember.
after looking over it though, it might have been 15 companies - not 20. sorry about that.
I passed on all the big consultancies (accenture, cgey,ibm, etc ) just because i really don;t like the corp culture too much. Personally, i am not too fond of the McK culture because it seems to be way bigger than it was a few years back..but it still does help for the resume in the long term. I have 3 of my interviews from the original list of the tier 1/1.5 consultancies above..and 2 other interviews from the firms in that secondary list.
I do agree with what people are saying about intervieiwng with more companies. I kinda started with the mentality of going McK/Bain (i am still interviewing with them), but a classmate mdae me realize that if i went to a smaller firm, I could probably move to partner much faster - if i intended to stay in consulting.