Which router does support DNS-O-Matic DynDNS service, out of the box, for sure?
With out of the box I mean without the need to install some other firmware as DD-WRT.
DD-WRT has a list of supported routers:
You can choose any of those, however I do recommend routers from Cisco (linksys) or D-Link. Not only are these competent routers, but are also very flexible inherently. I find that Verizon routers offers a very nice stock firmware.