Neural Architecture Search (NAS) represents an emerging machine learning (ML) paradigm that automatically searches for models tailored to given tasks, which greatly simplifies the development of ML systems and propels the trend of ML democratization. Yet, little is known about the potential security risks incurred by NAS, which is concerning given the increasing use of NAS-generated models in critical domains. This work represents a solid initial step towards bridging the gap. Through an extensive empirical study of 10 popular NAS methods, we show that compared with their manually designed counterparts, NAS-generated models tend to suffer greater vulnerability to various malicious attacks (e.g., adversarial evasion, model poisoning, and functionality stealing). Further, with both empirical and analytical evidence, we provide possible explanations for such phenomena: given the prohibitive search space and training cost, most NAS methods favor models that converge fast at early training stages; this preference results in architectural properties associated with attack vulnerability (e.g., high loss smoothness and low gradient variance). Our findings not only reveal the relationships between model characteristics and attack vulnerability but also suggest the inherent connections underlying different attacks. Finally, we discuss potential remedies to mitigate such drawbacks, including increasing cell depth and suppressing skip connects, which lead to several promising research directions.