I was walking around and being thane until I noticed a thief picking the lock to my door. I go to investigate and bam! He's in. Drawing my sword, I chase after him, but it turns out my loving wife and priestess of Dibella, Anwen, has already handled the would be robber. Uhm... I don't want her dying nor do I want anything valuable stolen. Do the thieves actually steal from your home?

Ive had a non-guild thief turn up in Riften before nicking stuff from the market stalls. I would suggest you put your highly valued possessions in the Riften house safe.

I've seen a couple thieves already being chased by guardsman and citizens in Riften after they tried to steal one too many pots and kettles from someone (pretty bad thieves, got themselves killed over stuff worth just one or two gold each). They almost make it out the front gates before the guards kill them, two bodies at the entrance now.

So yeah, not so nice a neighborhood

Every single time I go to Riften, the guards are killing a thief, and I mean EVERY. time.

The Riften house has a safe? Where?