We analyze the sharing of very short identity by descent (IBD) segments between humans, Neandertals, and Denisovans to gain new insights into their demographic history. Short IBD segments convey information about events far back in time because the shorter IBD segments are, the older they are assumed to be. The identification of short IBD segments becomes possible through next generation sequencing (NGS), which offers high variant density and reports variants of all frequencies. However, only recently HapFABIA has been proposed as the first method for detecting very short IBD segments in NGS data. HapFABIA utilizes rare variants to identify IBD segments with a low false discovery rate. We applied HapFABIA to the 1000 Genomes Project whole genome sequencing data to identify IBD segments which are shared within and between populations. Some IBD segments are shared with the reconstructed ancestral genome of humans and other primates. These segments are tagged by rare variants, consequently some rare variants have to be very old. Other IBD segments are also old since they are shared with Neandertals or Denisovans, which explains their shorter lengths compared to segments that are not shared with these ancient genomes. The Denisova genome most prominently matched IBD segments that are shared by Asians. Many of these segments were found exclusively in Asians and they are longer than segments shared between other continental populations and the Denisova genome. Therefore, we could confirm an introgression from Deniosvans into ancestors of Asians after their migration out of Africa. While Neandertal-matching IBD segments are most often shared by Asians, Europeans share a considerably higher percentage of IBD segments with Neandertals compared to other populations, too. Again, many of these Neandertal-matching IBD segments are found exclusively in Asians, whereas Neandertal-matching IBD segments that are shared by Europeans are often found in other populations, too. Neandertal-matching IBD segments that are shared by Asians or Europeans are longer than those observed in Africans. This hints at a gene flow from Neandertals into ancestors of Asians and Europeans after they left Africa. Interestingly, many Neandertal- or Denisova-matching IBD segments are predominantly observed in Africans - some of them even exclusively. IBD segments shared between Africans and Neandertals or Denisovans are strikingly short, therefore we assume that they are very old. This may indicate that these segments stem from ancestors of humans, Neandertals, and Denisovans and have survived in Africans.