This paper presents a vision for AGI-native wireless systems that go beyond 6G, aiming to enable next-generation wireless networks with artificial general intelligence (AGI) capabilities. The paper argues that current AI-native wireless systems, which rely on conventional AI tools like auto-encoders and neural networks, are insufficient to meet the complex requirements of emerging wireless use cases such as the metaverse, holographic teleportation, and cognitive avatars. These use cases demand real-time, high-quality, and reliable communication, computing, and AI capabilities that traditional wireless technologies cannot provide. To address these challenges, the paper proposes a new approach to AI-native wireless systems that incorporates common sense, enabling them to generalize and adapt to unforeseen scenarios. The proposed AGI-native wireless systems are built on three fundamental components: a perception module, a world model, and an action-planning component. The perception module abstracts real-world elements into generalizable representations, which are then used to create a world model based on principles of causality and hyper-dimensional (HD) computing. This world model is viewed as an HD causal vector space that aligns with the intuitive physics of the real world, a cornerstone of common sense. The world model enables analogical reasoning and manipulation of abstract representations, and drives the action-planning component of the AGI-native network. The action-planning component uses brain-inspired methods such as integrated information theory and hierarchical abstractions to enable intent-driven and objective-driven planning. The paper also discusses three use cases related to human users and autonomous agents: analogical reasoning for next-generation digital twins (DTs), synchronized and resilient experiences for cognitive avatars, and brain-level metaverse experiences exemplified by holographic teleportation. Finally, the paper concludes with a set of recommendations to ignite the quest for AGI-native systems, envisioning this paper as a roadmap for the next-generation of wireless systems beyond 6G.This paper presents a vision for AGI-native wireless systems that go beyond 6G, aiming to enable next-generation wireless networks with artificial general intelligence (AGI) capabilities. The paper argues that current AI-native wireless systems, which rely on conventional AI tools like auto-encoders and neural networks, are insufficient to meet the complex requirements of emerging wireless use cases such as the metaverse, holographic teleportation, and cognitive avatars. These use cases demand real-time, high-quality, and reliable communication, computing, and AI capabilities that traditional wireless technologies cannot provide. To address these challenges, the paper proposes a new approach to AI-native wireless systems that incorporates common sense, enabling them to generalize and adapt to unforeseen scenarios. The proposed AGI-native wireless systems are built on three fundamental components: a perception module, a world model, and an action-planning component. The perception module abstracts real-world elements into generalizable representations, which are then used to create a world model based on principles of causality and hyper-dimensional (HD) computing. This world model is viewed as an HD causal vector space that aligns with the intuitive physics of the real world, a cornerstone of common sense. The world model enables analogical reasoning and manipulation of abstract representations, and drives the action-planning component of the AGI-native network. The action-planning component uses brain-inspired methods such as integrated information theory and hierarchical abstractions to enable intent-driven and objective-driven planning. The paper also discusses three use cases related to human users and autonomous agents: analogical reasoning for next-generation digital twins (DTs), synchronized and resilient experiences for cognitive avatars, and brain-level metaverse experiences exemplified by holographic teleportation. Finally, the paper concludes with a set of recommendations to ignite the quest for AGI-native systems, envisioning this paper as a roadmap for the next-generation of wireless systems beyond 6G.