Free Open Source Components for Xamarin

Xamarin Forms
PaintView - Paint with touch
RangeSliderView - Slider with two handles to set a range of values
TableView - Bindable and templated table of any model
ImageViewer - Browse images in a slide show
VideoViewer - Download and play videos or stream from URL
PdfView - View PDF documents (in-app on iOS and with intent on Android)
DropDownView - Drop down for selecting from a collection of strings
Form Validation - Bindable and flexible form validation engine with an MVVM pattern

Xamarin Android
RepeaterView - Repeats items from a collection using an adapter pattern