Random Events could include things like the following:

1. Heavy rains have turned all the grounds acrross the land to a quagmire.  All armies have 50% movement for 3 turns.
2. Visiting Scientist in town, you have +20% science for 3 turns.
3. One of your underlings have assassinated a person from the <Faction>'s family.  You have -xxx diplomacy for 30 turns.
4. One of your family has married into the <Faction> family.  You hav +xxx dipomacy for 30 turns.
5. Magic Storms are ripping accross the continent.  All armies outside of cities take 2hp (multiply for number of men in squad etc)  per turn for 3 seasons.
6. A local ruffian has been organising dissent in <City Name> city.  That city has -20 corruption for 5 turns (reducing each turn by 4).
7. A worldy bard has stopped in the city of <City Name>.  The peopl have started a festival for the time he is there.  city has +5 gilder per turn for 3 seasons.
8. Your scientists have gotten careless and tried to use magic to scry for lost knowledge.  This has attracted the attention of (pick a magic enemy appropriate for the time into the game/or for the tech being researched).  The enemy will bee line for a city (and appear out of nowhere).  make sure the minimum time to reach the city is 6 turns.  Gives people time to get defenses there

That's all I can think of that I haven't seen already posted by others   I hope a couple make it into the game!!