Android: If you want your image backgrounds to blur or apply the Bokeh effect After Focus is a free and easy way to get effects usually reserved for much more expensive cameras.
After your shot is taken the app you can select which areas of your photo to blur and to what degree by drawing lines with your finger to indicate the point of focus. There are also several other image aftereffects.
There is a pro version for $1.75 that adds support for images up to 2048 pixels, edge-feathering, creating double photos and more filters.
If you want some of the effects of Instagram but don't want a social network experience this app might be up your alley. With over 6000 positive reviews on Google Play you may want to give it a try.