The integration of Artificial Intelligence (AI) in healthcare has introduced significant concerns regarding transparency, interpretability, and trust, particularly in high-stakes clinical environments. Explainable AI (XAI) has emerged as a pivotal solution to these challenges by providing interpretable insights into AI-driven decisions. This paper surveys both established and emerging XAI techniques with a focus on their applicability to healthcare domains. While traditional methods like LIME and SHAP are widely adopted, this work highlights novel and underexplored approaches such as concept-based, prototype-based, counterfactual, and knowledge-graph-based explanations. For instance, prototype-based networks have demonstrated improved interpretability in histopathology by extracting semantically meaningful tissue prototypes, achieving over 10% fidelity gain compared to conventional saliency maps. The survey spans diverse clinical applications including medical imaging, electronic health records (EHR), genomics, wearable devices, and robotics. Furthermore, it discusses domain-specific evaluation challenges such as the trade-off between interpretability and faithfulness, the absence of ground truth explanations, and the necessity for human-centered validation. Finally, the paper outlines key future research directions including multimodal XAI, causal reasoning, and user-centric system design. This comprehensive synthesis serves as a reference point for future XAI innovation in healthcare.