I'm trying to find a good, extensive corpus that uses "simple" or "basic" English, in the sense that it should be easily understandable to people who are not proficient in the English language. For examples, see Basic English and the Simple English Wikipedia. Do such corpora exist? Do you know where I can find a list of simple English corpora?
A dump of the Simple English Wikipedia makes a good and freely available corpus for Simple English.
For Basic English, there is a downloadable Bible in Basic English.
A "basic" or "simple" corpus is actually very hard to define. It's something we all assume exists when we get started in NLP, but come to realize is usually not feasible.
Every corpus has a purpose and a bias though. Make sure you're aware of these when using that corpus.
EDIT: A new corpus was just released today, English grammaticality judgments from nearly 700,000 subjects, (around 50% non-native speakers). Since you asked for "simple" English from less proficient speakers, you can filter by proficiency, e.g. number of years speaking English.