Some native speakers will tell you that expressions like “a couple things” are perfectly fine, others that “a couple” without “of” cannot be used at all. The truth is somewhere in between.
Although we may commonly hear “in a couple of hours” or “I saw a couple of people” in American English (as opposed to British English), in “written” English (i.e. English used in formal contexts such as essays, business correspondence, etc.) the only correct variant is the one with “of”:
- We will leave in a couple of days. (correct)
- We will leave in a couple of days. (ungrammatical American variant)
This is, of course, only true of “a couple” used in the sense of “several”. If we use it in the literal sense of “couple”, i.e. “two people”, it is not followed by anything, e.g. “they are a nice couple”. There is also one phrase in which “a couple” is always used without “of”, namely “a couple more”:
- I need a couple more cups of coffee. (correct)
- I need a couple of more cups of coffee. (wrong)