Fog of World is an app where you "track" where you have been. You earn badges from various places you've been and earn flags from the countries you visit. It's not really a competition since you don't connect with anyone online. All data is stored on your phone, so if you don't have it backed up and lose your phone you lose all your achievements. It encourages you to explore the world around you and encourages you to take a road less travelled.

Here are some pics:

It's pricey though but you pay once and the developer is awesome to support. I highly recommend it!