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By far the app/widget I use that attracts the most interest is Beautiful Widgets. Every time someone sees my Galaxy Note 2 phone or my Galaxy Note 8.0 tablet the first question they ask is, "what is that cool home screen widget?"
Beautiful Widgets is a customizable clock widget that can turn your device into a work of art. The hundreds of downloadable themes vary from the pure whimsical to the simply elegant, and every aspect of the appearance is user-configurable.
In addition to the clock widgets, the package also has weather widgets and system control widgets for turning things like wi-fi on and off from the homescreen. There is also an integrated weather app, accessed by tapping the weather section of the widget, that is excellent for seeing the forecast from your favorite weather service.
The Live Wallpaper shown in the image above is part of the package and besides being attractive, it shows the current weather conditions. The wallpaper changes with the weather condition so rain, snow, and other conditions are displayed to show the weather at a glance. It also varies with time of day, so the wallpaper slowly changes from daytime to night to provide an attractive screen that never gets boring.
Beautiful Widgets Pro — $1.99 (free version available with limited feature set)