The loss of telomere function can result in telomeric fusion events that lead to the types of genomic rearrangements, such as nonreciprocal translocations, that typify early-stage carcinogenesis. By using single-molecule approaches to characterize fusion events, we provide a functional definition of fusogenic telomeres in human cells. We show that approximately half of the fusion events contained no canonical telomere repeats at the fusion point; of those that did, the longest was 12.8 repeats. Furthermore, in addition to end-replication losses, human telomeres are subjected to large-scale deletion events that occur in the presence or absence of telomerase. Here we show that these telomeres are fusogenic, and thus despite the majority of telomeres being maintained at a stable length in normal human cells, a subset of stochastically shortened telomeres can potentially cause chromosomal instability. Telomere fusion was accompanied by the deletion of one or both telomeres extending several kilobases into the telomere-adjacent DNA, and microhomology was observed at the fusion points. This contrasted with telomere fusion that was observed following the experimental disruption of TRF2. The distinct error-prone mutational profile of fusion between critically shortened telomeres in human cells was reminiscent of Ku-independent microhomology-mediated end-joining.