I'm currently up to Floor 14 and whilst they are becoming harder to complete, there seems to be little happening in the way of progression (story wise at least).
So, like the title states, How many floors are there in Streetpass Mansion?
There are 50 floors. Once you defeat the final boss on the 50th floor, you have an option to play through again, keeping the weapon you had equipped for that boss.
This video shows the final boss fight, the ending, and the subsequent "Restart the game" option on the main menu.
I'm on 25, so there are at least that many. :) I'd be interested to hear how high up it goes, too.
There's at least 50. after you clear the 30th, you'll find out there's actually 50. I heard a rumor there's suppose to be 1000, but i do not know for certain. Currently on the 39 floor.