Who is eligible?
Pretty much everyone, unless you’re a convicted criminal. In that case, stop committing crimes. Classifying members as “low risk travelers”, Global Entry was intended to help Americans who don't routinely rob banks or kill people, but do frequent international destinations.
However, since there’s no minimum number of trips required to qualify, pretty much anyone with a passport can get Global Entry. So-called low-risk travelers also include docile Dutch citizens, South Koreans, Germans, and Mexican nationals.
So if I’m a US citizen, I'm golden?
Essentially. You’re only ineligible if: you lie on your application (which would be stupid, since this is a Federal program); are a convicted felon; have pending criminal charges or outstanding warrants; have been found in violation of any customs, immigration, or agriculture regulations or laws in any country; or are the subject of any sort of criminal investigation.