Learning Styles is an excellent overview of types of learning styles, their use in higher education, and using learning styles in teaching excerpted from a longer essay on addressing learning styles through technology.
Grasha's Five Teaching Styles describe the most prevalent ways faculty think about and approach teaching.
The Keirsey Tests are based on the Myers-Briggs Type Indicator. Limited profiles are offered for free on-line.
The Index of Learning Styles Questionnaire is a free inventory used to assess preferences on four dimensions (active/reflective, sensing/intuitive, visual/verbal, and sequential/global) of a learning style. This site has both web-based and paper-and-pencil versions of the inventory, response scoring sheet, descriptions of learning styles, and links to papers that discuss ways to address these styles through different teaching approaches (registration required).
VARK (Visual, Aural, Read/Write, Kinesthetic) Guide to Learning Styles is a popular, easy-to-use and easy-to-interpret learning styles inventory. The website contains background information on the questionnaire, advise to teachers on administering the questionnaire, and helpsheets for students on study practices keyed to VARK learning preferences.