Diagnostics in high energy density physics, shock physics, and related fields are primarily driven by a need to record rapidly time-evolving signals in single-shot events. These measurements are often limited by channel count and signal degradation issues on cable links between the detector and digitizer. We present the Ultrafast Pixel Array Camera (UPAC), a compact and flexible detector readout system with 32 waveform-recording channels at up to 10 Gsample/s and 1.8 GHz analog bandwidth. The compact footprint allows the UPAC to be directly embedded in the detector environment. A key enabling technology is the PSEC4A chip, an eight-channel switch-capacitor array sampling device with up to 1056 samples/channel. The UPAC system includes a high-density input connector that can plug directly into an application-specific detector board, programmable control, and serial readout, with less than 5 W of power consumption in full operation. We present the UPAC design and characterization, including a measured timing resolution of ∼20 ps or better on acquisitions of sub-nanosecond pulses with minimal system calibrations. Example applications of the UPAC are also shown to demonstrate operation of a solid-state streak camera, an ultrafast imaging array, and a neutron time-of-flight spectrometer.