The use of social networking sites (SNSs) is rapidly increasing as billions of individuals use SNS platforms regularly to communicate with other users, follow the news, and play browser games. Given the widespread use of SNS platforms, investigating the potential predictors of addictive SNS use beyond Facebook use has become paramount given that most studies so far focused on “Facebook addiction.” In this study, a total of 511 English-speaking SNS users (58.1% young adults aged 20–35 years; 64.6% female) were recruited online and asked to complete a battery of standardized psychometric tools assessing participants’ sociodemographic characteristics, SNS preferences and patterns of use, SNS addiction, preference for online social interaction, maladaptive cognitions, fear of missing out (FoMo), dysfunctional emotion regulation, and general psychiatric distress. Overall, about 4.9% (n = 25) of all participants could be classed as having a high SNS addiction risk profile. Moreover, the results further indicated that FoMo (β = 0.38), maladaptive cognitions (β = 0.25), and psychiatric distress (β = 0.12) significantly predicted SNS addiction (i.e., p < 0.0001) and accounted for about 61% of the total variance in SNS addiction, with FoMo providing the strongest predictive contribution over and above the effects of sociodemographic variables and patterns of SNS use. The implications of the present findings were discussed in light of extant literature on behavioral addictions and Facebook addiction and further considerations were provided regarding the potential clinical implications for cognitive-based psychological treatment approaches to SNS addiction.