Single patch quilts
A one patch quilt is a quilt that uses a single shape to create the whole quilt - so just squares or rectangles etc.
3, 4 and 9 patch quilts
These are quilts that have a unit that is split into 3 or 9 subsections which can be a single piece of fabric or several sewn together to create part of a pattern.
Art quilts are quilts intended to be a piece of art that is hung on a wall, usually with embellishments and not intended to be used in any other way.
These are a form of quilt that was first popular in Victorian times and is again popular amongst many quilters. They are made with many different kinds of fabrics at many angles, not all that would normally be used on quilts like velvet, the seams are often embroidered and many additional embellishments are added.
Paper piecing is a method in which you basically sew the fabric to a paper pattern and then at the end remove the paper before quilting.
Fan art quilts
These need no explanation.
As you can see there are many, many types of quilts on dA I hope you enjoyed the ones I shared here and hope that it will inspire you to consider making one yourself.