Generalizable dense feature matching in endoscopic images is crucial for robot-assisted tasks, including 3D reconstruction, navigation, and surgical scene understanding. Yet, it remains a challenge due to difficult visual conditions (e.g., weak textures, large viewpoint variations) and a scarcity of annotated data. To address these challenges, we propose EndoMatcher, a generalizable endoscopic image matcher via large-scale, multi-domain data pre-training. To address difficult visual conditions, EndoMatcher employs a two-branch Vision Transformer to extract multi-scale features, enhanced by dual interaction blocks for robust correspondence learning. To overcome data scarcity and improve domain diversity, we construct Endo-Mix6, the first multi-domain dataset for endoscopic matching. Endo-Mix6 consists of approximately 1.2M real and synthetic image pairs across six domains, with correspondence labels generated using Structure-from-Motion and simulated transformations. The diversity and scale of Endo-Mix6 introduce new challenges in training stability due to significant variations in dataset sizes, distribution shifts, and error imbalance. To address them, a progressive multi-objective training strategy is employed to promote balanced learning and improve representation quality across domains. This enables EndoMatcher to generalize across unseen organs and imaging conditions in a zero-shot fashion. Extensive zero-shot matching experiments demonstrate that EndoMatcher increases the number of inlier matches by 140.69% and 201.43% on the Hamlyn and Bladder datasets over state-of-the-art methods, respectively, and improves the Matching Direction Prediction Accuracy (MDPA) by 9.40% on the Gastro-Matching dataset, achieving dense and accurate matching under challenging endoscopic conditions. The code is publicly available at https://github.com/Beryl2000/EndoMatcher.