As per the title, is the proper usage "ongoing" or "on-going" when writing something such as ongoing research projects?
Either is acceptable, though the form
ongoing is almost uniquely the one used in modern times. (The hyphenated version, as with most compound words in English, was the original form; the hyphen got dropped after time as the word became more common.)as
The Online Etymology Dictionary gives the following origin:
also on-going, 1877, from on + going (see go).
This link provides some guidance. To quote:
This word never has been hyphenated, but people think that it is a mix of ‘on’ and ‘going’, but if you think of someone ‘going on about grammar’, you would not say that that person was ‘ongoing’!