The problem is that if you use the verb "to be" you need to add a predicative, such as a noun or an adjective, to describe what the subject is. An example using adjectives is
It's quite often sad/scary/reassuring to hear such rumors these days.
And an example using nouns is:
It's quite often a surprise / a nightmare / a miracle to hear such rumors these days.
If you don't notice the problem with the original sentence, maybe the following trick can help.
In all these sentences, the logical subject is the phrase "to hear such rumors these days". Try to change the order, putting this phrase at the beginning, thus getting rid of the "it", and at the same time removing other unnecessary parts ("quite" and "these days"): the "core" of the sentence is
To hear such rumors is often.
Do you notice, now, that something is missing? It would be natural to ask: "...It is often what?"
So, you need a predicative. A possible solution, as Ashwin Schumann suggested, is to replace "often" (which is an adverb and can't be a predicative) with "common" (which is an adjective and therefore can):
It's quite common to hear such rumors these days.
An alternative solution, if you don't want to change the word "often", is to use another verb, for example "happens" instead of "is":
It happens quite often to hear such rumors these days.
This verb doesn't require a predicative and therefore the sentence is correct.