We describe CrowdLogging, an approach for distributed search log collection, storage, and mining, with the dual goals of preserving privacy and making the mined information broadly available. Most search log mining approaches and most privacy enhancing schemes have focused on centralized search logs and methods for disseminating them to third parties. In our approach, a user's search log is encrypted and shared in such a way that (a) the source of a search behavior artifact, such as a query, is unknown and (b) extremely rare artifacts---that is, artifacts more likely to contain private information---are not revealed. The approach works with any search behavior artifact that can be extracted from a search log, including queries, query reformulations, and query-click pairs. In this work, we: (1) present a distributed search log collection, storage, and mining framework; (2) compare several privacy policies, including differential privacy, showing the trade-offs between strong guarantees and the utility of the released data; (3) demonstrate the impact of our approach using two existing research query logs; and (4) describe a pilot study for which we implemented a version of the framework.