And also, a slightly ~educational post as I'll go through all the types.
So, the basic definition of a spiral is gliding across the ice with the free leg above hip-level, usually in arabesque position. It is a required element in ladies and pairs skating. They require not only flexibility but immense control and balance.
The two main types of spirals are unassisted and catchfoot. They are also categorized by edge (but I find that unnecessary).
Unassisted
Arabesque
Fan
Charlotte
Catchfoot
Basic Catchfoot
Kerrigan Spiral
Y-Spiral
Two-Handed Biellmann
One-Handed Biellmann
These Are NOT Spirals
I-Spin
Catchfoot Layback
And now I'm going to be selfish and just picspam my favorite spiral-ers
Alissa Czisny
Eliot Halverson
For your time, here's a beautiful montage of Michelle's classic change of edge spiral: