The proliferation of geospatial data in urban and territorial environments has significantly facilitated the development of geospatial artificial intelligence (GeoAI) across various urban applications. Given the vast yet inherently sparse labeled nature of geospatial data, there is a critical need for techniques that can effectively leverage such data without heavy reliance on labeled datasets. This requirement aligns with the principles of self-supervised learning (SSL), which has attracted increasing attention for its adoption in geospatial data. This paper conducts a comprehensive and up-to-date survey of SSL techniques applied to or developed for three primary data (geometric) types prevalent in geospatial vector data: points, polylines, and polygons. We systematically categorize various SSL techniques into predictive and contrastive methods, discussing their application with respect to each data type in enhancing generalization across various downstream tasks. Furthermore, we review the emerging trends of SSL for GeoAI, and several task-specific SSL techniques. Finally, we discuss several key challenges in the current research and outline promising directions for future investigation. By presenting a structured analysis of relevant studies, this paper aims to inspire continued advancements in the integration of SSL with GeoAI, encouraging innovative methods to harnessing the power of geospatial data.