We present an overview of the ‘ICE’ hardware and software framework that implements large arrays of interconnected field-programmable gate array (FPGA)-based data acquisition, signal processing and networking nodes economically. The system was conceived for application to radio, millimeter and sub-millimeter telescope readout systems that have requirements beyond typical off-the-shelf processing systems, such as careful control of interference signals produced by the digital electronics, and clocking of all elements in the system from a single precise observatory-derived oscillator. A new generation of telescopes operating at these frequency bands and designed with a vastly increased emphasis on digital signal processing to support their detector multiplexing technology or high-bandwidth correlators — data rates exceeding a terabyte per second — are becoming common. The ICE system is built around a custom FPGA motherboard that makes use of an Xilinx Kintex-7 FPGA and ARM-based co-processor. The system is specialized for specific applications through software, firmware and custom mezzanine daughter boards that interface to the FPGA through the industry-standard FPGA mezzanine card (FMC) specifications. For high density applications, the motherboards are packaged in 16-slot crates with ICE backplanes that implement a low-cost passive full-mesh network between the motherboards in a crate, allow high bandwidth interconnection between crates and enable data offload to a computer cluster. A Python-based control software library automatically detects and operates the hardware in the array. Examples of specific telescope applications of the ICE framework are presented, namely the frequency-multiplexed bolometer readout systems used for the South Pole Telescope (SPT) and Simons Array and the digitizer, F-engine, and networking engine for the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX) radio interferometers.