The vision of 6G requires autonomous, intelligent, and adaptive systems that can manage complex and dynamic communication environments. In this context, artificial intelligence (AI)-based agents are seen as key enablers, combining perception, knowledge, decision, and execution functions to operate across distributed network layers. This study provides a comprehensive overview of agentic systems for 6G, examining their architecture, core capabilities, and enabling AI techniques. We propose a novel framework for agentic intelligence levels which conceptualizes agentic AI systems as a gradual and multidimensional spectrum. Additionally, trust and governance levels, which characterize system deployability independently of agentic competencies, are introduced. We analyze how methods such as reinforcement learning (RL), federated learning, graph neural networks, transfer learning (TL), and meta-learning can be integrated into agents to support tasks including network optimization, predictive traffic management, spectrum allocation, energy-efficient resource control, and security enhancement. The potential of foundation model-based agents in 6G networks is examined, comparing them to classical RL-based agents to highlight their complementarity. Practical 6G use cases—including smart resource orchestration, environmental coordination, industrial applications, reliability and security assurance, and situational awareness—are presented to demonstrate the applicability of agents in real-world scenarios. Their strengths, limitations, and complementary roles within agent-based frameworks are highlighted. The current technological and industrial maturity levels of use cases are mapped to the proposed levels of agentic intelligence and trust/governance. The study bridges theoretical advances and practical 6G implementations by linking AI methods with concrete deployment challenges. Finally, the study identifies challenges related to scalability, interoperability, explainability, and trust, and highlights future directions for building reliable, adaptive, and ethically aligned agent-based systems in 6G.