AFW (Android Folder View) is a neat little widget inspired from KDE's Folder View that you can use to view files on your homescreen and open them in their respective applications. It currently displays a maximum of 16 files (one for each cell).
Features a [untested] way to open files with no extensions (picture 3).
At the moment there is no automatic refreshing or a dedicated button for it so updates must be carried out by resizing the widget (if you change the settings or the folder content).
To resize/refresh hold your finger on the widget until it becomes active, but instead of dragging it to the trash bin lift your finger to release it, then grab it from the resizing corner, drag it around a little and release. Finally click back to exit the resize mode.

Screenshots: