I would assume most distros accept individual private donations (they may also accept free hosting). However, that is probably not the bulk of their financing in most cases.
Note that some of the major distros may have some paid staff, and possibly also office space, the cost of which likely exceeds that of hosting the repos1. This should not be taken to mean that they are not primarily volunteer based (except for the commercial variants, they are), just that they do have operating budgets.
Fedora is owned by Redhat, and the latter is a publicly traded, billion dollar annual business. I would presume they do quite a bit to help support the former.
According to wikipedia, CentOS is now also owned by Redhat and earlier this year Redhat announced their ongoing sponsorship of CentOS development.
Ubuntu is owned by Canonical, which I do not think is on a par with Redhat, but they probably still have revenues into the tens of millions USD per year. Last time I downloaded an image, Ubuntu was pretty aggressive about encouraging you to make a small donation at the same time. $5 a year would I think cover the costs of repo hosting associated with the average installation.
The Debian project has been around for nearly 20 years and surely has a substantial core of users willing to help support it. They also have a list of "partners" here which provide them with resources. I would think Canonical helps out significantly, since Ubuntu is reliant upon Debian, but judging from this link provided in Kiwi's answer, they are still having to beg publicly for $250K to cover meeting costs, which is pretty disappointing.
Arch is likely much poorer than the other distros mentioned here, but they may still collect enough money from various sources to support some development staff and hosting. They do not appear to obviously solicit on their site, so I would guess this funding comes mostly from industry (and possibly, government) grants.
1. To get some idea of how much this hosting would actually cost, consider that GNU/Linux systems probably account for 1-2% of desktop systems worldwide and at least 40% of web servers. If we then assume this might amount to ~25 million systems, if a large (theoretical) distro accounted for 10% of those and each user accounted for 4 MB a day averaged out over time, this would amount to 10 TB/day. I would think if you know the right people, you could perhaps get 3000 TB/month for <$5000 US.