A longstanding challenge in microfluidics has been the efficient delivery of fluids from macro-scale pumping systems into microfluidic devices, known as the "world-to-chip" problem. Thus far, the entire industry has accepted the use of imperfect, rigid tubing and connectors as the ecosystem within which to operate, which, while functional, are often cumbersome, labor-intensive, prone to errors, and ill-suited for high-throughput experimentation. In this paper, we introduce TapeTech microfluidics, a flexible and scalable solution designed to address the persistent "world-to-chip" problem in microfluidics, particularly in organ-on-a-chip (OoC) applications. TapeTech offers a streamlined alternative, utilizing adhesive tape and thin-film polymers to create adaptable, integrated multi-channel ribbon connectors that simplify fluidic integration with pumps and reservoirs. Key features of TapeTech include reduced pressure surges, easy priming, rapid setup, easy multiplexing, and broad compatibility with existing devices and components, which are essential for maintaining stable fluid dynamics and protecting sensitive cell cultures. Furthermore, TapeTech is designed to flex around the lids of Petri dishes, enhancing sterility and transportability by enabling easy transfer between incubators, biosafety cabinets (BSCs), and microscopes. The rapid design-to-prototype iteration enabled by TapeTech allows users to quickly develop connectors for a wide range of microfluidic devices. Importantly, we showcase the utility of TapeTech in OoC cultures requiring fluid flow. We also highlight other utilities, such as real-time microscopy and a well-plate medium exchanger. The accessibility of this technology should enable more laboratories to simplify design and setup of microfluidic experiments, and increase technology adoption.