Drupe would like you to think that contacts on Android, and on mobile in general, are broken. They're not - phone makers and developers have been doing this for a while, after all - but that doesn't mean that they can't be improved upon. Drupe is a "floating" app that puts contacts, and the means to do all sorts of interesting things with them, in a unique overlay accessible from any other app. Check it out in action in the video below.
To activate Drupe, just tap the translucent triple-dot activation point in any app. A list of your favorite contacts (or groups of contacts) will appear along the left side of your phone's screen, with a list of communication apps on the right. Slide a contact over to an icon and the corresponding app will open with a new call/text/email/Facebook message/whatever to the contact you selected. Neat, huh? It's an interesting approach, especially for people who use their phones for communication more than for browsing Reddit and playing 2048. (Like I do.) Even some oddball activities, like navigating to an address in maps, are supported.
Drupe is well thought out: for example, swiping in the open space of the overlay will switch the contact list between your favorites and your most recently-contacted, and it has an integrated search if you can't find your contact in either of those lists. An impressive array of configuration options include showing or hiding specific apps, customizable themes, and the ability to switch between a full drag-and-drop action or a directional swipe (handy for big phones). The app is free with no in-app purchases.