Besides the usual Google apps, the 6 apps that I use most are:

- Remote Desktop Client" by Xtralogic -- the best Windows Remote Desktop client I've found on Android, and it supports Network Level Authentication (which most of the others don't) so you can connect to the latest versions of Windows desktop and server in the most secure way. WAY worth the money I paid.
- "IP Cam Viewer" by Robert Chou, so my wife can watch our pets when we're not home -- constantly updated and improved. Definitely worth the money.
- "K-9 Mail" mail client by K-9 Dog Walkers, so that I can check my Hotmail account - blows away the stock Android mail client! Free.
- "Audible" audio book player by Amazon. Free.
- "Visual Voice Mail" by T-Mobile. Free. (I've heard that Verizon charges extra for similar functionality)
- "Thinking Space Pro" by Mindjet, for idea brainstorming. Compatible with FreeMind data files. Very unique menu system. Worth the money!

Article source: http://www.zdnet.com/photos/10-indispensable-android-apps/6341259