Are there any databases that describe which printer* needs which toner?
You do not say for what kind of printers (brand or how they are connected), or at what level, home or business.
I know of no multi-printer application for home use, nor would that normally be an issue since it is not hard to figure out supplies for one or two printers. Even so, many of these printers, if they are Ethernet connected, had a web page at their IP address, where you can look at how much they have consumed, or there is an application, which can give you supply information, that comes with it, and that will sit in the systray.
In a business enterprise, there are a few options. One is if you have an SNMP monitoring application, some have printer "SNMP traps". This guy actually wrote his own that you could use:
In businesses, HP printers are still the kings, and are widely-deployed. You could use their Jetadmin software to look at them.
(not the supplies tab)
http://h20338.www2.hp.com/hpsub/cache/332262-0-0-225-121.html (there also used to be a report-generation plug-in, but the link is broken).
Such a database unfortunately does not exist. One has to do the grunt-work of searching for the toner per printer type. My own experience is that for the future health of the printer, it is better to use the toner from the manufacturer, even if costlier. Using price-comparing sites or even amazon.com, one can with a bit of luck find special deals.
We use FMAudit. It also provides alerts when printer are out of the ink/toner/consumables that they require.