Thanks for the information. At least I am not the only one with this problem.
I have found three issues with the emails.
1. Emails from Magento Community. every email from Magento - Open Source eCommerce receives a warning from my antivirus software (avast!) that the email has a suspicious subject.
2. Emails from the Magento webshop sent to myself: all emails seem to be blocked at my email hosting company. These are sent through the email servers that belongs to my email account hosting company. They use a ‘standard setup for spam and virues’. I can chose to select an external epost server. Unforunatelely, I have no experence in doing this, and I am not sure what to look for to find a solution.
3. Emails from the Magento webshop sent to customers: I assume that any real customers will have the same problem - i.e. that they will not receive the order confirmations etc. from my Magento webshop.
Obviously it is important to find a stable solution for this problem. Unfortunately I lack the knowledge to do anything more than to report the issue.