Hey Tanja,
We just built an app to do exactly this! It sends product recommendations (including new products) to customers and has zero setup. It also tracks sales so you can see how many orders you get from these auto-pilot emails. A store today got a sale within 30 seconds of activating the app. You can't beat that!
Matthew raises some good points, and we automatically manage frequency and the other issues he raised so everything is handled for you.
You can install the app here http://concierge.sendicate.net/
Have fun with it.
Thanks
Chad