They most certainly do. Not as good as a USMLE in my opinion. This topic was recently covered. Take a look below.
Not sure who DOESN'T take them but my guess would be the highly competitive programs would just screen people based on a USMLE score and toss a COMLEX in the dumpster. Thats a guess.
Most of the large Universities (Mayo, Iowa, Cleveland, Hopkins) that I called all took the COMLEX, but they also said they liked/preferred to see the USMLE too because it made it simplier for them to compare me as an applicant.
Programs want to compare apples to apples, not apples to oranges. However validated the Comlex is, really dosent matter. It doesnt help programs pick applicants because they cannot compare you directly to allopathic students,