I think there is a difference between something being done subconsciously (without conscious thought or decision) and something happening by second-nature. I suspect that non-verbal spells, for wizards on the level of Voldemort and Dumbledore, are second-nature, in that such wizards are so deeply immersed in and at one with their magic. Where one stops and the other begins is hard to pinpoint.
I think Dumbledore's non-verbal spell during the duel with Voldemort in OOTP was indeed an example of this. So other examples I can think of that may possibly be this kind of magic are the Trace and Taboo (no incantation for either, but there are parameters involved that trigger magic to occur. In the case of the Taboo, it's the magical relaying of information; in the case of the Trace, it's a tracking/reporting system of sorts). There doesn't seem to be an incantation for sending a Patronus to deliver a message, as Expecto Patronum conjures a regular shield Patronus. As Death Eaters cannot conjure Patronuses, this messenger capability seems to be for the Order only. In DH, as DVK mentions, there is Harry's wand acting of its own accord against Voldemort in chapter four. And last but not lease there's, of course, the mother of them all: Lily's protective enchantments that she passes to Harry upon her choice to die instead of step aside and let Voldemort kill her son.
NOTE: Yes, the HP Wiki says that the spell Harry used in The Seven Potters against Voldemort was a disarming charm; however, the Wiki is incorrect. The spell is unnamed, but is described as He felt it drag his hand round like some great magnet, saw a spurt of golden fire through his half-closed eyelids, heard a crack and a scream of fury.