HIV rapid diagnostic tests (RDTs) combined in an algorithm are the current standard for HIV diagnosis in many sub-Saharan African countries, and extensive laboratory testing has confirmed HIV RDTs have excellent sensitivity and specificity. However, false-positive RDT algorithm results have been reported due to a variety of factors, such as suboptimal quality assurance procedures and inaccurate interpretation of results. We conducted HIV serosurveys in seven sub-Saharan African military populations and recorded the frequency of personnel self-reporting HIV positivity, but subsequently testing HIV-negative during the serosurvey. The frequency of individuals who reported they were HIV-positive but subsequently tested HIV-negative using RDT algorithms ranged from 3.3 to 91.1%, suggesting significant rates of prior false-positive HIV RDT algorithm results, which should be confirmed using biological testing across time in future studies. Simple measures could substantially reduce false-positive results, such as greater adherence to quality assurance guidelines and prevalence-specific HIV testing algorithms as described in the World Health Organization's HIV testing guidelines. Other measures to improve RDT algorithm specificity include classifying individuals with weakly positive test lines as HIV indeterminate and retesting. While expansion of HIV testing in resource-limited countries is critical to identifying HIV-infected individuals for appropriate care and treatment, careful attention to potential causes of false HIV-positive results are needed to prevent the significant medical, psychological, and fiscal costs resulting from individuals receiving a false-positive HIV diagnosis.