I know of two main Exile archetypes that are capable, both of which rely upon run economy engines: Pawn, also known as "Streetchess", and MKUltra/Black Orchestra, also known as "Conspiracy".
---Streetchess has been removed by rotation. This is his first archetype, by which players would combine Pawns with Deep Red, Scheherazade, and Technical Writer. Each trigger, which may occur on each successful run, nets one card draw and about 1-4 credits, which also allows for click compression by triggering successful runs on archives. This engine is reliant on the amount of ice the corp player protects his central servers with, making it weaker to glacier archetypes. However, it is a very strong counter to asset spam, as it can easily and uncounterably trigger successful runs on unprotected assets, combined with the usually less protected centrals of the asset spam archetype, to create a late game click compression and run economy surpassing any other.
---Conspiracy is the modern, although weak, iteration of the Exile archetype, as it lost many of its combo pieces to rotation. This installs MKUltra and maybe Black Orchestras from the heap, (using Sahasrara, Cybsoft MacroDrive, and/or Dhegdheer to reduce their install costs), to place credits on Technical Writers and sell them later to Aesop's Pawnshop. Reliant on the ice composition and arrangement of the corp player, as you would be influenced on running certain servers over others. Requires large amounts of memory. No significant strengths or weaknesses.
Outside of these archetypes, Exile pairs well with recurring temporary programs, such as Cerberus "Lady" H1 and Nyashia.
May also be used with Panchatantra, Sharpshooter, and Deus X recursion breaking, although that archetype is very weak.