Are pilots at Airlines typically assigned to fly a single Type in a given month / year or do they get switched routinely between multiple types of aircraft as per scheduling convenience?

i.e. Is it common to, say, fly a B-747 & then return flying a B-777 etc. 

How about more extreme changes like switching between Boeings & Airbuses or Turbojet / Turboprop etc.? 

I guess that begs the question whether pilots typically are certified & current across multiple Types? How common is this?

I'm looking more for comments about what is operating practice across airlines rather than a hard rule, which I guess does not exist.