Civ switching -- that is, having a new set of unique buildings to build, new units to train, new civics to learn -- is fun for me. It really reinforces to me that this age / era is quite different from the age that preceded it. Sit up in my chair, rub my hands together, have a good think about what to do next.
Era transitions -- that is, buildings changing yields, units being replaced and relocated, IP disappearing, resources changing -- are also both impactful and fun. As the progress meter approaches 75%, I give serious consideration to what I can, or cannot, finish before the age ends. Can I get that wonder finished? Can achieve this legacy path and not that one? Should I take an enemy city, or pack up into the commander and return home? Are any of my cities at risk of flipping?
An example: As Antiquity was ending, I knew that my scouts would not survive into Exploration. I sent them out swimming, mapping the coastline, to see if I had any short (1-tile) passages to an island. Yes! More importantly, one of the city-states I had befriended would be in EXCELLENT position to receive Treasure Fleets. Rather than start a war which would require Influence to support, I used up my influence to incorporate that CS into my empire. Yes, it put me over the settlement limit, but not for very many turns.
Since I know what will happen in the era transition, I plan for it. I ensure that my commanders are healthy and packed. Even after XX years between ages, I will have land units to deploy; nearly all of my settlements will have the ranged unit that I left in them for defense. Don't start things, late in the age, that I can't finish.
