[subject] + 常常 + [verb phrase]
[condition] + [subject] + 往往 + [verb phrase]
通常 + [subject] + [verb phrase]
[subject] + 通常 + [verb phrase]
常常, 往往 and 通常 all say something happens a lot. 常常 counts how often, 往往 states a pattern seen under certain conditions, and 通常 says what the normal case is.
往往 sums up past experience: when X, Y tends to happen. The sentence names the X – a time, a place, a kind of person. Without it, 往往 sounds unfinished.
往往 describes what has been true. A request, a plan or a wish takes 常常.
通常 can go before the subject as well as after it, and it can describe a noun: 通常情况下 "under normal circumstances". It says what is standard and leaves room for exceptions.
The negative of 常常 is 不常: 我不常去.