Anomaly detection has traditionally dealt with record or transaction type data sets. But in many real domains, data naturally occurs as sequences, and therefore the desire of studying anomaly detection techniques in sequential data sets. The problem of detecting anomalies in sequence data sets is related to but different from the traditional anomaly detection problem, because the nature of data and anomalies are different than those found in record data sets. While there are many surveys and comparative evaluations for traditional anomaly detection, similar studies are not done for sequence anomaly detection. We investigate a broad spectrum of anomaly detection techniques for symbolic sequences, proposed in diverse application domains. Our hypothesis is that symbolic sequences from different domains have distinct characteristics in terms of the nature of sequences as well as the nature of anomalies which makes it important to investigate how different techniques behave for different types of sequence data. Such a study is critical to understand the relative strengths and weaknesses of different techniques. Our paper is one such attempt where we have comparatively evaluated 7 anomaly detection techniques on 10 public data sets, collected from three diverse application domains. To gain further understanding in the performance of the techniques, we present a novel way to generate sequence data with desired characteristics. The results on the artificially generated data sets help us in experimentally verifying our hypothesis regarding different techniques.