Following precedent, I should start by saying I have no formal training in music. However, unlike the precedent, that constitutes only a small part of my "have not"s in music. So, regarding what I say below...Beware!
In the original question, by "good" counterpoint, I meant counterpoint that
you think is good.
I believe Pat is right that there is no consensus on the definition and usage of many terms related to the topic. Outside the academic sense, I think the term contrapuntal has another and quite established "colloquial" use, to loosely denote any of the notions of being rhythmically independent, counter-melodic or polyphonic.
I also agree with Pat that in the academic context, any two or more simultaneous musical lines constitute a counterpoint (like any speech constituting prose), whether conforming or not to any set of formal counterpoint rules. To further complicate things, the counterpoint discipline, unintuitively, has rules even for a single melodic line.
As to Jer's remark on horizontal vs vertical: I believe it is the Renaissance music where the harmony is incidental to/byproduct of practicing the (modal) counterpoint rules of the period to provide smooth flow of (mostly) independent voices. This is in contradistinction, generally speaking, to the harmony-conscious, 'standard progression seeking' tonal counterpoint of the Baroque.
It seems, besides the advent of monody and homophony (hence the figured bass), polyphony remains alive and well in the Baroque but as distinct from the former period it is more meter-conscious, rhythmically driven and built on tonal (harmony) counterpoint, though modal polyphony does not totally wither away.
Again, I agree with Pat that there is a grey area between monody/homophony and polyphony, across which a piece may move when, for instance, its ostinato/broken-chord like main accompaniment to the melody gradually starts acquiring a life of its own.
Of counter melody and Mahler 2: Yes, thanks a lot for bringing forth this beautiful passage (violins&celli) where both the melody and countermelody are quite tuneful, the sort that is dear to my heart

. I tend to think this one as the Type where the counter melody elaborates and complements the main melody. Another example would be, imo (from 22:30)
https://www.youtube.com/watch?v=r0AK_50-9rQyet another (from 15:42)
https://www.youtube.com/watch?v=-4788Tmz9ZoThere is, imo, another type where the two melodies don't even live in the same town, which I love even more (from 14:07)
https://www.youtube.com/watch?v=QIHFfuzKYPIwhile there, another one which starts like the first type but then, enters the mezzo
https://www.youtube.com/watch?v=c8BBsf51bYUAll the above are to my best but, to repeat, quite limited understanding of the subject. I also hope I have managed to articulate my thoughts without offending or disappointing anyone for I aim none of such but don't always succeed.
