Can spilling a liquid on a keyboard or other input device connected to a desktop computer damage the computer itself?
It is possible, but it does not usually happen. A full short at a USB or PS2 ports would mostly effect the 5V signal, possibly damaging the port itself. But isolation just due to the layers of components in there usually keeps a full short from damaging back further than the port itself.
A crossup of the 5v to the serial lines data entry really would not be a big issue, as the components wouldn't have a big problem taking the higher voltage for a while at the input, so usually once recovered the data will then again be recognised if the device is still powered.
It would so totally depend on the computer build itself and the conductivity of the liquids. I guarantee that a motherboard could be made so poorly that it would.
Now with the new USB3 specs and its higher power, the possibilities become more endless http://www.everythingusb.com/superspeed-usb.html
Remember that in many cases, pulling the keyboard, and putting in another, can require a restart or power off, so if your trying another keyboard, after messing up the one you were using, shut the computer off, put in other keyboard, then turn back on.
Most specifications don't require protection against shorts, but most devices have them anyway. The USB specification requires full protection in the host or hub against damage from shorts. Two caveats:
This only applies specifically to USB. For other standards, some have such protection (RS232, eSATA) and some don't (PS/2 keyboard).
There are a few stories where people swear a short damaged their hardware. This could be due to devices that don't comply with the specification or it could be due to devices that were already fairly broken and would have failed anyway. As far as I know, there are no controlled studies.
On a modern computer with a USB-connected keyboard, or even with the old PC/PS2 keyboards, it's exceedingly unlikely that spilling a beverage on a keyboard would damage anything other than the keyboard. (If it were likely I would have done it several times.)
You very likely will damage the keyboard itself, of course, and, in particular, carbonated beverages are bad, as are beverages containing sugar or cream. Plain black coffee is not quite as bad, and plain water probably won't cause serious permanent damage once the keyboard has dried out for several days. (It takes a minimum of 3-4 days for a keyboard to dry after getting wet, and sometimes a week or so.)
If you spill a carbonated beverage on a keyboard the only way to rescue it is to immediately disassemble the keyboard as much as possible and rinse the keyboard "innards" well with 2-3 changes of distilled water. Then set it up leaning against something (so the water will run out) to dry for a week or so.
Mice are probably even less likely to transmit damaging surges. The biggest danger would be with devices that have separate power supplies attached, but even there the USB port itself is well-protected, so damage would be unusual.
The only times (twice in in 40-odd years) I've ever seen external surges damage a computer it was due to lightning strikes to ethernet or phone cables.