While travelling, my Argonian Shaman Drekius-ra-jei enjoys "waterfalling". Basically you travel exclusively by waterway and when you reach a waterfall you jump off and hope like hell that you'll land in a deep part of the water. Serious fun if playing Dead = Dead. Notable places include Valtheim Towers bridge (not strictly a waterfall) and a waterfall North west of Whiterun (seriously no landmarks I have no clue where it was)
My other character the Khajiit assassin Mufasa enjoyed rearranging items in people's houses and collecting statues of Dibella - I think he was slightly OCD...
I forgot to add my third character the vengeful Dunmer vampire-mage; he likes to stack things (buckets, cabbages etc) on posts/rocks and throw a fireball at them to watch them fly.
So what does YOUR character do for fun?