In Fred Anderson's "Crucible of War: The Seven Years' War and the Fate of Empire in British North America, 1754-1766" there is one specific mention of a "smallpox blanket".

In the instance in question, a British captain named Ecuyer was defending a fort (Fort Pitt) sieged by Indians during an Indian uprising called "Pontiac's Rebellion". After a parley he gifted the leader of the Indians several items, among which were two blankets and a handkerchief from the fort's smallpox hospital. This is obviously a "smallpox blanket".

Did Ecuyer understand what he was doing? Probably yes. While the 18th century's understanding of viral diseases is not as good as our modern one, they did understand contagion. Clear evidence is the usage of inoculation (a crude predecessor of vaccination. You deliberately infect yourself with smallpox in a way that will lead to a lighter outbreak). So he probably understood that his actions would lead to a smallpox outbreak among Indians that may or may not kill an undetermined number of natives.

So smallpox blankets were actually a thing. Another question is how “widespread” they were. Well, “Crucible of War” contains 11 mentions of smallpox (I love ebooks’ search function). Many are about outbreaks among the British and colonials. 2 are about Indians taking “trophies” (aka as captives and scalps) after the fall of Fort William Henry. The garrison had been suffering from smallpox, so in their quest for renown, the natives spelled their own doom. 1 is about the incident described above.

The next mention is most interesting. Again during Pontiac's Rebellion, the British commander for North America (Amherst) gave his officers the order to spread smallpox among the Indians in order to “reduce” them, obviously hoping it would cripple their war effort.

Unfortunately, I do not know whether that order was actually put into practice, appaling as it is to even suggest it (at least to people of the 21st century). Neither do I know anything about possible applications during the 19th century, which is the era most people think of when they think of “Indians” (and great plains and buffalos and dancing with wolves).

So, to sum it up: Did it happen? Yes. Was it widespread? Possibly (at least after the 7 Years War). However, you should keep two things in mind, before you jump to judgements. A) most of the interaction between native Americans and non-native Americans was not during war. E.g. the US government did use atomic bombs (another WoMD). But that was a big exception made in wartime and is obviously not the rule. Similarly, the British were at war at that time and were desperate. B) Colonials were suffering from smallpox as well (otherwise there would have been no infected blankets in the first place). These infections were not orchestrated by anybody, but were just bad luck. Similarly, smallpox can also spread naturally to and among Indians.

Small edits for clarifications.