I have read around about this, in Riverwood when you talk to Gerdur she gives you a key to her house. Some people are saying that you can store things there with no problem while others say you have to buy a house. Is there a clear answer on this?
The Help Section is Pretty explicit about this:
from System > Help > Containers
Do not leave items in containers you do not own! They may not be there when you come back for them. If you want a place to store items permanently, consider buying a house.
from System > Help > Houses
After purchasing a house, you can safely leave your items inside- They will always be there when you return
In addition, one of the messages in the loading screens states that the only true safe place to store items is in storage in your homes.
I've had food and ore stored in the chest near the bed, in that house. I forgot about it while questing and buying a house in Whiterun. Much later I came back to Riverwood and my loot was still there.
On the other hand I've had some stolen items that I couldn't sell stuffed into a barrel outside the blacksmith in Whiterun and those disappeared after a couple in-game days.
Seeing as Gerdur's house is the first "homebase" for adventuring in Skyrim, I would be surprised if the developers didn't flag that house's containers as permanent.