There's lots of reasons why the US has military basis around the world, some are for exclusively their own benefit, some for the benefit of the countries where they are and some for both. Some of the reasons are:
- Some of the countries are very poor and they just need the money
- Diplomatically it is always a smart move
- Hosting the US army is strengthening the national defense
- The UN is backing up the US claims in most of the cases
- The local constitutions can't stop the US from making the bases
- The US snagged a lot of territory after the WWII
- Once the USA defeats an enemy they mark their territory
- Some countries ask for them and welcome them
- Once there's a base it is extremely hard to move it away...