1. You are walking along a path and you see a dead body. As you approach it to check it for loot or see what is happening a couple of things could happen:
A. It's an ambush and the body is not dead but armed and grabs you while his friends jump out of bushes and attack.
B. Ambush #2 and a carefully placed net nabs you and you will have to cut or burn (fire spell) yourself out and fight your attackers.
C. It's a set up and guards placed it there to frame and extort the one who touched it. They ask you to pay a huge bribe. You can try to kill them and face whatever consequences can come of that. Or this could turn into a quest for revenge or justice.
2. It's storming out and lightening strikes a branch and falls on someone you cross on a remote path. You can help them if you are strong enough, get help for a reward, or loot their body and leave them to die... but he survives and wants vengeance.
3. A Hunter asks you to help him track a wounded deer but the quest takes you into a serious pack of wolves who is wanting to feast on its flesh. Well now you're stuck and have to fight for your freedom.
4. I've mentioned this on the Elder Scrolls discussion board before but... you are walking near a river and you see a headless body floating down stream. You investigate and a side quest appears for you to figure out. You head up stream and see another headless body stuck in the reeds. Heading further upstream brings you into the cause of this...
5. A near naked man(or men) is running your way screaming and yells something along the lines of "run for your life!" As you continue you see shed armor and weapons on the ground. Later a scorched body and this leads you to a dragon or powerful wizard who is either extremely proficient in destruction magic or conjuration.
6. As your walking along a path an arrow flies in your direction and hits a tree near your face. A voice tells you to back off or you'll get one in the face. This brings up the conversation menu and through shouting your conversation back and forth you conclude that the person is guarding a treasure of some sorts. You can escort him to safety or take advantage of him.
7. You hear word of a siren who can sing a man into sleep. Then she loots your body and leaves you to wake up confused several hours later, and naked. Ear plugs bought at a store will help you to track her down and get justice. Nice guy: knock her down and shove a rag in her mouth and apprehend her so the guards can take her, silence her then jail her. Bad guy: kill.
8. A trail of gold coins... is it a trap or something good???
Other random events.
You see wolves chasing deer and avoid you for the more tasty lunch.
Bandits ambushing guards and vice versa.
Avalanches and rock slides.
More natural occurrences