Though there are cheaper options for iOS, (e.g., Screens), LogMeIn is the best remote-desktop option for Android devices. There are two ways to move your PC's cursor: by pushing a desktop around a fixed cursor, or by dragging a cursor across the screen. Other gestures let you zoom and access a QWERTY keyboard.
WIRED Adjust color, compression, and resolution for sharper performance. Mac and PC compatible.
TIRED Only the iOS version offers file sharing. Pricey.