To start down the customization path, Themer is an Android launcher -- a kind of skin for your device which allows you to install custom themes. There are hundreds of free and premium themes to choose from, which allow you to change elements including screen backgrounds, icons and widgets.
If you enjoy your art and want your phone to reflect this in an active way, consider downloading Muzei. The app gives users an array of live wallpaper to choose from, whether you want to see popular works of art or a montage of your own photos.
Light Flow goes beyond customizing backgrounds and sounds; instead, the app taps into the potential of your LED lighting -- used for notifications -- and allows you to experiment. The app gives you the option to set different LED variables depending on an event; for example, if you receive a text message one color then another could flash. You can also control other events such as missed calls, email notifications, low battery alerts or when you enter a signal-less zone. The app can also be used to customize vibration patterns for notifications.
UCCW is a customization app which focuses on widgets. Without requiring a launcher, the app allows you to add custom clocks, battery meters, weather alerts, text objects and calendar widgets on your homescreen. What makes this app particularly interesting is the inbuilt WYSIWYG editor which lets you customize layouts, fonts and images used in widgets.
Nova Launcher is a launcher I tend to use to customize my phone with skins and themes. Nova's strength is its ease-of-use; while you pay for the app if you're keen on customization it is well worth the money. The launcher allows you to customize themes, colors, backgrounds, app drawers and widgets -- and does not slow down your smartphone to do so. Once downloaded, there are free and premium Nova-compatible themes and icon packs available in the Google Play store.
Finally, despite the sheer size of customized templates, icons and widgets available for Android smartphones, I am yet to find many widget designs which compare to those on offer by Beautiful Widgets Pro. The app, which costs a few dollars, gives you a library of widgets, clocks and weather tabs for devices of various screen size -- and attention has been paid to details in each widget.