I've sung in domes with wonderful acoustics--like the Rotunda of the U.S. Capitol (protest songs during a sit-in demonstration in the '70s)--and horrible acoustics--an oval shaped "multipurpose room" in the student union at the College of William and Mary in Williamsburg, Va. The walls were carpeted with sound-absorbent felt. It's the only time I've heard the combination of an acoustically dead space with an echo.
I've found all sorts of wonderful reverberant spaces: at Yale University in New Haven, Conn., there's the Harkness Chapel in Branford College (all stone, 30 feet long by 30 feet wide by 50 feet high!) and the small stone room underneath the Marquand Chapel at the Yale Divinity School. Since then, I've found places like the dome outdoors at the Canadian Embassy on Pennsylvania Avenue, NW in Washington, D.C. (actually, there are a lot of domes in Washington, D.C.)
A few years ago, I sang with the Kartuli Ensemble (which specializes in the a cappella choral music of the Republic of Georgia) on a tour through the Eastern Midwest of the U.S. and we found one acoustic gem of a space after another. Heinz Chapel at the University of Pittsburgh and the Center Meeting House at Shakertown in Pleasant Hill, Kentucky stand out. The Shaker meeting house is so acoustically live a space that when you come into it or leave it, even with just ambient silence, you notice the acoustic difference. It was built to magnify the sounds within, like a giant sound box, and reports from the 19th century were that singing within could be heard from a distance of 2 to 3 miles away. Our chorus listened to a performance of Shaker music, and were so taken with the acoustics that we asked if we could try them out with a song from our repertoire. The reverberations were marvelous. Then we went on to tour the rest of the restored Shaker village. When we got to the Center Dwelling House, the curators and costumed interpreters in the basement welcomed us, heard that we had sung in the meeting house, and said that they were looking forward to hearing us on the third floor. We had no idea what they were talking about. But each of us, sooner or later, made his way to the third floor, and discovered there another meeting room with resonant acoustics. It was only a matter of time before enough of us gathered to start singing there. The folks in the basement heard us! And we dinally found out what they meant.
There are other times when I've encountered acoustics that just make you want to do a VERY long set so you can try out everything in the acoustically wonderful space.
I've also had the experience, like Musicman and Hank, of singing and bringing out harmonics. While it's certainly much easier to do in an acoustically resonant space, it can be done anywhere if you're really in tune. The Kartuli Ensemble recorded an album in a studio space with those foam fingers on all the walls--a space designed to stifle any resonance, which could then be added in later electronically, or so the engineer said. He was astonished when we kept producing harmonic overtones among us. All it takes is to be REALLY in tune, with a very focussed sound. But good acoustics help--we've sometimes figured out the natural resonating pitch of a performing space and deliberately tuned our singing to that key, which brings out overtones like nobody's business.