However, "I took GRE" yields over 66,000 hits on Google, whereas "I took the GRE" only shows about 44,000.
So either I'm wrong (possible) or more non-native speakers take the GRE than native speakers (also quite possible).
It could also have something to do with "I took GRE classes" or sentences like that.
"I took GRE yesterday" - 587
"I took the GRE yesterday" - 241
"I took SAT yesterday" - 2
"I took the SAT yesterday" 157
So...maybe more NNSs are taking the GRE and writing about it on the internet, while more NSs are taking the SAT and writing about it on the internet?