Instagram, the most popular photo-filter app, doesn't allow to right-click and download images to your computer.
However I have found a trick that works when using the desktop version of Instagram):
1. Right-click on the Instagram picture that you want to download.
2. Select "view source".
3. Click CTRL+F (Command+F in Macs)
4. Type JPG to find where the picture URL is.
5. Copy the first result link and paste it in your browser address, click enter.
6. Now you can download the Instagram picture that you wanted.