Why does the United States military have bases in other countries but other countries don't have bases in the United States? What are the odds of another country putting a base in the US?

A lot of countries host bases for other countries. There are a few advantages to this.

• First - Base leases usually come with money. Most countries like to have money come in.
• Second - Base leases usually come with favors or otherwise improve relationships between the countries. Want to influence a powerful country? Hosting one of their bases is a good way to do it.
• Third - Bases provide defense.

The US doesn't host much in the way of foreign forces because none of those things are terribly important to them. The US pretty much exclusively plays the role of patron rather than client. The US does host some small numbers of foreign forces, but only for the purposes of training. The US would probably not be happy hosting any of the countries with global aspirations, because they are exactly the countries they would be the most concerned about attacking the US.