This app lets you measure the point-to-point (great-circle) distance between two or more waypoints on a map or measure the surface area defined by a polygon having three or more points as its corners.
It uses online maps so it needs an internet connection.

Tap and hold to set a new waypoint, tap the options icon to read the manual or to open the settings view to change the map type or the measuring unit. You can choose between (kilo)meters, feet/yards/miles and nautical miles. The options menu also lets you choose to go to the Save/Restore view.

Tap the calculated measurement at the bottom of the map to switch between feet/yards/miles or meters/hectometers/kilometers.

The Pro version is exactly the same as the free version except that (by popular demand) it won't display any ads.