There's no better way to experiment how a UI library works than trying it hands on. Many UI library projects provide example apps that are great for exactly that. These apps will give you a good understanding about functionality in real life on real devices. If you're a dev you can present these examples to your designers and let them see what kind of functionality and interaction is available out of the box.
What makes it even better is that source code for these apps is available. If you need any of this functionality simply download the source and use it as an example implementation.
ActionBarSherlock is one of the most useful libraries around. The demo app has tons of examples of different functionality including action bar navigation, fragments, loaders and even service broadcasters.
This is another ActionBarSherlock app. This one is demonstrating action bar styling.
ViewPagerIndicator example lets you see and feel how different view pager indicator configurations work.
Pull-to-Refresh for Android
Example app link (apk)
This example app lets you try out pull-to-refresh functionality on a list.
|(direct link to APK)|
GreenDroid example app lets you experiment with the rich functionality the library provides. These include custom item views, action bar, segmented bar, quick actions image viewers and pagers.
Hansel and Gretel Sample
See how fragment bread crumbs work with this example app.
AndroidQuery Demo Snippets
This library isn't UI library but I decided to include it in the list anyways. It includes tons of example samples for network communication XML parsing etc.
Android UI Patterns
No home page available
No Source Code available
Author of this app has gathered multiple open source library project into one app. Some of the projects are outdated and I recommend doing a little bit googling for alternatives before you commit to any of the libraries here. The app still gives you a chance to experiment with multiple different libraries to see how they work with you.
Note that even the app is named very similarly as my blog it is not done by or affiliated with this blog.