Have a look in the source:
http://core.trac.wordpress.org/browser/trunk/wp-includes/class-wp-customize-control.php
Basic control types:
- text
- checkbox
- radio
- select
- dropdown-pages
Also some advanced control types (as-described by Otto):
- WP_Customize_Color_Control – extends the built in WP_Customize_Control class. It adds the color wheel jazz to places where color selection is needed.
- WP_Customize_Upload_Control – This gives you an upload box, for allowing file uploads. However, you probably won’t use this directly, you’ll extend it for other things… like:
- WP_Customize_Image_Control – This gives the image picker and the uploader box. It extends the upload controller. You can see it in action on the custom background piece, where a user can upload a new file to be the background image.
- WP_Customize_Header_Image_Control – Because of the resizing action of the header piece, it needs a bit of special handling and display, so the WP_Customize_Header_Image_Control extends the WP_Customize_Image_Control to add that functionality. You can see it in action on the custom header piece, where a user can upload a new file to be the header image.
Also:
- WP_Customize_Background_Image_Control
If you need more than that, you’ll have to define your own, custom control.