GPUs have a natural affinity for streaming applications exhibiting consistent, predictable dataflow. However, many high-impact irregular streaming applications, including sequence pattern matching, decision-tree and decision-cascade evaluation, and large-scale graph processing, exhibit unpredictable dataflow due to data-dependent filtering or expansion of the data stream. Existing GPU frameworks do not support arbitrary irregular streaming dataflow tasks, and developing application-specific optimized implementations for such tasks requires expert GPU knowledge. We introduce MERCATOR, a lightweight framework supporting modular CUDA streaming application development for irregular applications. A developer can use MERCATOR to decompose an irregular application for the GPU without explicitly remapping work to threads at runtime. MERCATOR applications are efficiently parallelized on the GPU through a combination of replication across blocks and queueing between nodes to accommodate irregularity. We quantify the performance impact of MERCATOR's support for irregularity and illustrate its utility by implementing a biological sequence comparison pipeline similar to the well-known NCBI BLASTN algorithm. MERCATOR code is available by request to the first author.