The first HANA deployments were all analytical use cases like Datamarts and Data Warehouses because the benefits are there right out the box. EDWs like SAP BW run like lightening with a simple database swap.
With a transactional application like Finance or Supply Chain, most things run a little better from a simple database swap (SAP claim 50% faster for their own core finance). The real benefits come when logic from the applications are optimized and pushed down to the database level, from simplification of the apps (SAP is building a simplified version of their Business Suite), or from ancillary benefits like real-time operational reporting, real-time supply chain management or real-time offer management.
Best of all, unlike the other database systems in the market, HANA supports all applications on the same instance of data at the same time. No more copying, transforming and re-organizing data all over the enterprise to meet the needs of different applications. HANA perfectly serves the needs of all applications with one “system of record” instance.
SAP have provided a Use Case Repository that catalogues the various use cases for HANA.