A wide range of applications, including bioinformatics, time series, and log analysis, depend on the identification of repetitions in very long sequences. The problem of finding maximal pairs subsumes most important types of repetition-finding tasks. Existing solutions require both the input sequence and its index (typically an order of magnitude larger than the input) to fit in memory. Moreover, they are serial algorithms with long execution time. Therefore, they are limited to small datasets, despite the fact that modern applications demand orders of magnitude longer sequences. In this paper we present RACE, a parallel system for finding maximal pairs in very long sequences. RACE supports parallel execution on stand-alone multicore systems, in addition to scaling to thousands of nodes on clusters or supercomputers. RACE does not require the input or the index to fit in memory; therefore, it supports very long sequences with limited memory. Moreover, it uses a novel array representation that allows for cache-efficient implementation. RACE is particularly suitable for the cloud (e.g., Amazon EC2) because, based on availability, it can scale elastically to more or fewer machines during its execution. Since scaling out introduces overheads, mainly due to load imbalance, we propose a cost model to estimate the expected speedup, based on statistics gathered through sampling. The model allows the user to select the appropriate combination of cloud resources based on the provider's prices and the required deadline. We conducted extensive experimental evaluation with large real datasets and large computing infrastructures. In contrast to existing methods, RACE can handle the entire human genome on a typical desktop computer with 16GB RAM. Moreover, for a problem that takes 10 hours of serial execution, RACE finishes in 28 seconds using 2,048 nodes on an IBM BlueGene/P supercomputer.