There is one crucial aspect of this issue that has not yet been mentioned, but before I get to that...I concur with what has been posted by some other members.
Corydoras species tend to live as conspecifics in most of their habitats, being geographically isolated; but it is not uncommon to also find two species in a geographical area. They live in groups of hundreds, and that does seem to be the significant aspect. Others have mentioned the "chum around together" behaviour of cories of different species and the chumming of members of the same species. While some species do spend more time together, given the opportunity, they do also seem to enjoy mixing company.
The dwarf species are best kept alone, as one or two other members mentioned. They do tend to form "friendships" with upper fish much more than most of the larger sized species.
Corydoras hastatus is frequently seen in a shoal mixed in with a shoal of small-sized characins (tetras especially). The dwarf species also need more in the group than the larger cousins, though the larger the group the better for all of these fish. This issue of numbers really does make a difference to the well-being of the fish.
The only real negative to mixing species is hybridization, and this is the issue not yet mentioned in this thread. Someone posted the article on an aquarist in Europe maintaining species in his basement tanks that would be used to restock the habitats. It is unfortunate that we are today seeing the largest extermination of species in millions of years. Keeping the gene pool of a
Corydoras species pure is crucial; it may very well soon be the case that the only living members of a species are those in aquarists' tanks.
What this means is that those of us who keep multiple species must absolutely never introduce fry into the hobby beyond our own tanks. In their habitats, there is no evidence of hybridization, and the geographical isolation I mentioned above is unlikely to result in hybridization. But there is now plenty of evidence that species within the same lineage will hybridize when placed together in the artificial confines of an aquarium. I have concrete examples of this within my own cory aquarium. But I am cognizant that these fry must never leave my tanks alive.
There are now over 160 described species, and dozens more "C" and "CW" numbered fish awaiting scientific study that may or may not turn out to be distinct species, with the polyphyletic genus
Corydoras. A polyphyletic clade (here a genus) is a group of organisms (here, species) derived from more than one common evolutionary ancestor or ancestral group and therefore not suitable for placing in the same taxon. By contrast, a monophyletic clade is a group of organisms (again species here) descended from a common evolutionary ancestor or ancestral group, especially one not shared with any other group. Biological taxonomy aims to classify all species within a monophyletic genus, as this has benefits to our understanding of the species.
Phylogenetic analysis by several ichthyologists over the past few decades (subsequent to the discovery of DNA in the 1970's) have identified nine distinct lineages with the family Corydoradinae. This family includes the genera
Aspidoras, Brochis, Corydoras and
Scleromystax; all nine lineages are represented in the present
Corydoras genus. See Britto (2003), Ferraris (2007), Tencatt et al. (2013), Barriga S. (2014), Sarmiento et al. (2014), Tencatt et al. (2014), Tencatt & Pavanelli (2015), Tencatt & Evers (2016), Tencatt & Ohara (2016), Tencatt et al. (2016), and DoNascimiento et al. (2017).
- The genus Scleromystax initially erected as a subgenus of Callichthys by Günther (1864) and then made synonymous with Corydoras by Nijssen & Isbrücker (1980), was resurrected by Britto (2003) for Corydoras (now Scleromystax) barbatus and a couple of other species, and there are now 8 described Corydoradinae species and 8 undescribed "CW" numbers in this genus.
- Britto (2003) synonymized the three Brochis species into Corydoras and these, along with two other Corydoras species and a few "CW" numbers, now comprise lineage 8.
- A recent study by Luiz Tencatt (unpublished so not taxonomically "accepted" yet) of Aspidoras has proposed moving one species into Corydoras, leaving the remainder as lineage 2 (16 described and 3 undescribed species).
Species now placed within each one of these lineages are very likely to hybridize in the aquarium, something very unlikely to occur in the wild beecause of the circumstances such as those I already referenced. Responsible aquarists realize the situation here, and act accordingly; we do not need to be adding to the already overwhelming degradation of nature.
I will explain the lineages more if anyone asks.
) I bought a couple of cories, not knowing they needed friends (the person at the shop said they'd be fine with only 2 
