Cerberus lets you remotely track, lock and set new passwords, disable, take photos and have them uploaded to you, and sound an alarm in case your phone is lost or stolen. The app can inform you if the SIM card gets changed, and tell you the new phone number. It will tell you any Wi-Fi networks it connects to and the IP address of those networks. It will show you a record of where they have been. You can send messages to the phone, which will be displayed on the screen no matter what they're doing, or even if you've locked them out. You can access their call logs and message logs, and record audio and video. Also, the app is hidden from view and cannot be uninstalled by others without entirely wiping the phone. Which, if you like, you can opt to do remotely.
AdAway blocks advertising across the operating system.
AirDroid lets you browse your phone's files through a web interface either through a shared local network, tethering wireless devices to your phone, or in the latest beta through the web.
Glympse lets you send a link to someone informing them of your location in realtime, letting them track you for a duration of your choosing.
Sixaxis Controller allows you to use a PS3 controller as a gamepad. Also supports emulation of touchscreen input for games that don't natively support gamepads or keyboards.
tTorrent Pro is the best torrent application I've found on Android.
Spotify and Uberhype for streaming music; the latter for new trending tracks.