I want to use a new modem-router to replace one fried by a power surge. Snake-bit by that, I checked out the voltage for the new unit's adapter. It's supposed to be 12V, 600ma. Using a volt-ohmeter, I get 17V, no-load. Input is 120-121V AC. If I plug this in to the modem-router, will the load take care of this higher-than-needed voltage?
If the power adaptor was supplied with the modem-router, I would assume that the manufacturer intended them to be used together, so they should work together with no problem.
Most wall-warts are just brute-force unregulated transformer-rectifier-filter AC to DC converters with pretty poor (about 30% to 40% no-load to full-load) regulation, but if the adapter came with the router, then it should settle down to 12V plus or minus whatever the spec is when it's loaded by the router. To find out, measure the voltage when they're mated and powered up, as Ignacio Vazquez-Abrams suggested.
On the dark side, since the wall-wart's output obviously isn't regulated and you have mains voltage surges which have earlier fried kit, there's no guarantee that that won't happen again unless your new router - or the supply - sports some sort of surge protection.
If I were in your shoes, what I'd do would be to contact the manufacturer of the router in order to find out what the adapter's output looks like under various surge conditions and what the router's power input can survive.