I will tackle this questions in two steps: first, findings by researchers and teachers, then an alternative approach.
Grammar Instruction in Isolation Is Not Effective
In 1974, E. Hatch ("Second language learning - universals" in: Working Papers on Bilingualism, 3) made a distinction between "data-gatherers" and "rule-formers". Data-gatherers tend to focus more on the development of fluency rather than accuracy, while rule-formers adopt a more analytic, rule-based approach. A study by Suzanne Graham (Effective Language Learning, 1997) found that problems can arise when a data-gatherer is encouraged to take a more analytical approach to grammar learning (e.g. the German case system). On the other hand, learners who had been categorised as rule-formers later appeared to have developed elements of data-gathering.
There have also been studies comparing grammar courses on the one hand with grammar courses combined with an additional communicative component on the other hand. One such study is: Carol Montgomery & Miriam Eisenstein, 1985: "Reality Revisited: An Experimental Communicative Course in ESL", TESOL Quarterly, 19.2.
The researchers found that learners who had the additional communicative module made greater progress in accent, vocabulary, grammar and comprehension than the other group. What's more, the area in which they made the greatest improvement was grammatical accuracy!
In 2001, an article entitled "To Grammar or Not to Grammar: That Is Not the Question!" pointed out that the importance that the public attaches to traditional grammar instruction is based on an incorrect learning theory, i.e. the idea that "if teachers teach something well, students will learn it and, what’s more, will apply it well". However, grammar rules and grammatical analysis do not transfer well to writing and speaking for most learners.
Teaching traditional grammar in isolation from writing (or communication in general) is not very effective. Instead, it is more effective to refer to grammatical concepts in response to specific difficulties that learners experience in their writing, and to present examples of effective writing. (This is not an isolated finding. See also, e.g. "Effectively Teaching Grammar: What Works (and What Doesn’t Work)".)
An Alternative Approach to Grammar Exercises
So don't get carried away by grammar exercises madness. It's not a matter of what you feel comfortable doing (cf. the first point in Alicja Z's answer) but what helps you acquire the language.
If you really feel the urge to do grammar exercises, I recommend that you use them in a way that helps you leverage your "data-gathering" (cf. E. Hatch, above). For this, I suggest the following process:
- Do the exercises, then look at the corrections (or discuss them
with a tandem partner).
- Then, instead of moving on to the next batch of exercises, take each exercise or sentence that you answered incorrectly or that has a solution that you find unusual, and turn it into a cloze test.
- Enter each cloze test in a spaced repetition system such as Anki or Mnemosyne. (In other words, you turn the grammar exercises into flashcards. You can also do this on paper.) Some sentences can even be turned into more than one cloze test.
- You then review your flashcards on a daily basis. The spaced repetition system will space out the "exercises" in time depending on how easy (or hard) it is for you to solve them.
Note that you will need to "feed" the spaced repetition system with new flashcards every few days. The content does not need to come from grammar books only; you can also use other sources, such as newspaper articles, novels, etc. (And obviously, you can add vocabulary flashcards to the same deck, so you get some variation in your flashcards.)
This way, the grammar exercises become a form of input that leverages your data-gathering abilities. Over time, you acquire the grammar without necessarily learning the rules explicitly.