Hero - Duncan MacLeod is an example of the "Catalyst Hero" type. He doesn't change very much himself through what we've seen of his Quest, but we do see those around him change in response to his personality. I believe the Catalyst Hero requires stronger secondary characters to be engaging and successful as an on-going series. However, all of that aside, Duncan MacLeod is the closest reflection here of the idealized Arthurian Hero.

Mentor - Connor MacLeod and Joe Dawson are both Mentors we see in episodes, as is Darius. Duncan MacLeod seems to have had a fair share of other Mentors in his long life as well.

Herald - The Call to Action for an Immortal is the Final Gathering.

Shadow - MacLeod is Shadowed both by the Final Gathering and by the Watchers, whose knowledge of Immortals he considers a danger to himself and others.

Shapeshifter - Cassandra is an obvious Shapeshifter, reflecting as she does some portion of MacLeod's anima projection. At the young age when he first met her, she was probably very much an idealized "perfect" complement. Older, beautiful, and with mysterious powers and talents.

Trickster - Amanda, Fitzhugh, and others offer comic relief and consistently challenge MacLeod's world view. Methos is also a Trickster, offering occasional comic relief and serving to upset MacLeod's "status quo" by largely refusing to play by the rules of Immortality. His motives are also unclear, most especially in the early episodes but almost every time he appears. Neither MacLeod, nor anyone else, can ever be sure what Methos is going to do.

Threshold Guardian - Kalas, Kronos, assorted k'Immies. Each battle that MacLeod faces is a step toward the end of his Quest. The Dark Quickening is also a Threshold Guardian, forcing MacLeod to face his own inner problems and fears.

I really wasn't able to find a centrally important archetype for the Richie character. The "sidekick" is a well-known fictional type but there is no clear parallel for such a character in mythology, except the Ally.