Spam has become an important problem for computer security because it is a channel for the spreading of threats such as computer viruses, worms and phishing. Currently, more than 85% of received e-mails are spam. Historical approaches to combat these messages, including simple techniques such as sender blacklisting or the use of e-mail signatures, are no longer completely reliable. Many solutions utilise machine-learning approaches trained using statistical representations of the terms that usually appear in the e-mails. However, these methods require a time-consuming training step with labelled data. Dealing with the situation where the availability of labelled training instances is limited slows down the progress of filtering systems and offers advantages to spammers. In this paper, we present the first spam filtering method based on anomaly detection that reduces the necessity of labelling spam messages and only employs the representation of legitimate e-mails. This approach represents legitimate e-mails as word frequency vectors. Thereby, an email is classified as spam or legitimate by measuring its deviation to the representation of the legitimate e-mails. We show that this method achieves high accuracy rates detecting spam while maintaining a low false positive rate and reducing the effort produced by labelling spam.