Social media is becoming an inseparable component of our daily lives --- with the promise of providing an avenue for building connections with others worldwide. However, persuasive media coverage suggests that in reality, online social media is falling short of promises to provide a space for meaningful connections and interactions. Given that the landscape of social media is ever-changing, it is important to periodically probe into people's social media experiences to identify the challenges and nuances of how people make connections with others and experience the content that social media provides. To explore people's social media experiences, in this work, we conducted a qualitative exploratory study in which we took a two-pronged approach: (1) we created two small technology probes to elicit people’s thoughts and comments on how alternative features and functionalities could change how they use social media, and (2) conducted one-on-one creativity sessions to encourage our 16 study participants to explore how social media impact their lives and how it might transform in the future. The participants openly and enthusiastically discussed their experiences, connections, and agency on social media. Our findings suggest that the participants want features to increase expressivity, the ability to control content curation, and opportunities to make connections beyond what current social media platforms provide. We discuss the impact of privacy and anonymity in shaping social media experiences as well as the tension among agency, relevance, content curation, and echo chambers.