These days, ornamental turners working in wood often use a rose engine lathe to produce their artistic pieces. But there are other ornamental turning options which do not use a rose engine lathe.
Also, there are some really nice ornamentally turned pieces made on a "traditional lathe". A classic example is the Chinese Nested Sphere pictured to the right.
David Springett's book, Woodturning Wizardry is an excellent resource for such work. These books are very useful also:
This is an interview with Claude Lethiecq about Chineese nested spheres. It was recorded at the 2010 AAW symposium.
David Springett made this video in 2008 about elliptical turning on a lathe.