HgCdTe and InGaAs linear-mode avalanche photodiodes (APDs) were fabricated and tested for properties suitable for high-speed photon counting when integrated with commercially available 2-GHz resistive transimpedance amplifiers (RTIAs). The 2.71-μm, 100-μm-diameter HgCdTe APDs were fabricated in using an n + /p vertical carrier transport architecture designed to reduce carrier drift time and facilitate high-speed operation. At 215 K, a gain of 100 was measured with an excess noise of 2.5. The InGaAs/InAlAs APDs were fabricated using two absorber alloy compositions, one optimized for 950-1300 nm operation and the other for 950-1550 nm operation. Both were fabricated using multiple, cascaded gain regions that allowed for high gain and low avalanche-induced shot noise. Gain exceeding 6000 was observed, and the excess noise factor was measured to be below 20 at a gain of M = 1200 (effective k ~ 0.03). The InGaAs/InAlAs APDs were integrated into receivers consisting of a multi-gain-stage APD coupled to a commercial 2-GHz RTIA and were operated as thresholded photon counters. At a linear gain of M = 1800, a single photon detection efficiency greater than 85% was measured at a maximum count rate of 70 MHz; at a linear gain of M = 1200, single photon detection efficiencies greater than 20% were measured at maximum count rates of 80 MHz. At the temperature tested, 185 K, the receiver's dark count rate (DCR) is dominated by electronic amplifier noise from the TIA for low threshold settings, and by dark counts from the APD at high threshold settings.