I myself use Android (tablet and phone) and my favourite app is currently the AWD launcher EX on tablet... it has a hide-able dock which helps keep the screen clear and also has a few transitions etc to choose from as well as themes but all the themes I've tried so far mess up the dock image so I still use the stock one.
I'm an iPhone gal, so these are all Apple... and I have no idea if any of these apps are available for any other devices.
My Personal Favorites (you can click the links for more information - they open to new tabs/windows):
SoundHound (FREE or ad-free for $6.99) Bakodo (FREE or $0.99 for the Pro version) WolframAlpha ($2.99) iMathematics (FREE or $2.99 for the Pro version) Medscape (FREE, but requires an account through Medscape, which is also free)
for android: Advanced task killer, color flashlight, evernote, goggles, huffington post, M. Calendar (for ladies), Mighty Grocery, pocket auctions, spotify, tweetdeck, the word, yelp
There's loads of apps I feel I have to install when I get a new android phone...
Advanced Task Killer
Android System Info (shows battery, memory and disk space in widget)
Apps 2 SD (stores apps on the SD card)
Circle Launcher Light (tidies apps on home screen)
History Eraser
Memory Monitor
Unified Remote (controls PC remotely)
Volume Control+ (volume lock and scheduler)
Where's My Droid (helps you find your lost phone)
Wifi Analyzer
