James Stewart, author of calculus texts, has a $24 million house. It has lots of curved walls. Problem: find their areas or volumes, by integrating.
Simmons Hall, an MIT dorm opened in 2002, has a lot of oddly shaped rooms. (I found this silly, because the curved walls meant wasted space -- but I didn't live there, I just had friends who did, so it didn't bother me too much.) The story goes that the Cambridge fire department had trouble giving them a certificate of occupancy because they couldn't determine the volume of certain rooms and therefore couldn't determine whether they were adequately ventilated.
(Article from the Wall Street Journal; link from Casting Out Nines.)