Three mentalities have emerged in analytics. One view holds that reliable analytics is impossible without high-quality data, and relies on heavy-duty ETL processes and upfront data curation to provide it. The second view takes a more ad-hoc approach, collecting data into a data lake, and placing responsibility for data quality on the analyst querying it. A third, on-demand approach has emerged over the past decade in the form of numerous systems like Paygo or HLog, which allow for incremental curation of the data and help analysts to make principled trade-offs between data quality and effort. Though quite useful in isolation, these systems target only specific quality problems (e.g., Paygo targets only schema matching and entity resolution). In this paper, we explore the design of a general, extensible infrastructure for on-demand curation that is based on probabilistic query processing. We illustrate its generality through examples and show how such an infrastructure can be used to gracefully make existing ETL workflows "on-demand". Finally, we present a user interface for On-Demand ETL and address ensuing challenges, including that of efficiently ranking potential data curation tasks. Our experimental results show that On-Demand ETL is feasible and that our greedy ranking strategy for curation tasks, called CPI, is effective.