Hi, interesting topic! (:

Well, I can speak 3 foreign languages (at an upper-intermediate/ advanced level) and I'm currently learning two more languages and in my opinion you can't speak a language without studying the grammar rules. If you think about your mother tongue, you can speak it well now because, as a kid, you were taught grammar rules. I think the best way to learn a language is to follow the natural process of a language acquisition (that is the natural way children learn their native language: listen and THEN speak). But that's not enough (-: at the age of 5/6 children go to school to learn the basic rules and then their awareness about the language improves.

That's what I do when learning a language and I'm very content with my results (-:

I don't believe in extremes. I'm a native English speaker studying Spanish. I would say that because some of the grammar concepts are similar in both languages, for me knowing some Spanish grammar is not necessary, but has been helpful.

A good example is the positive and negative imperative in Spanish. I started off using Rosetta Stone, which is 100% immersion, 0% grammar. They somehow expect you to pick up the difference just by listening. I couldn't do it. Maybe if they had spent a couple of hours of lesson time on nothing but the positive and negative imperatives, I could have learned it that way. When I used a human teacher who explained them to me using grammatical terms, it became much easier.

The problem is that remembering rules means you are working with your left brain, and it interferes with fluency. It would be better to internalize them and make them automatic. But if I am trying to speak Spanish and my right brain does not automatically guide me as to whether to say ser or estar, it is better for me to remember "DOCTOR, Description Occupation Characteristics Time Origin Relationships," than to freeze, or say the wrong one.

One of the odd things is that I effortlessly use and understand half-a-dozen or so past verb tenses in English, and yet that's the sort of thing that is much better done by practice than by rule. The truth is that you can get by perfectly well in English just with "past, present, and future." Using the best verb tense is like using the best word choice--it's nice, but not necessary.

This is very interesting topic! I have some thoughts about it.

I learned two languages (English and Hungarian) on my own (almost without studying grammar, I just read and listened a lot). Also I tried to think in these languages (I artificially suppressed my thinking process in my native language and made random sentences in my head over and over again). What are my final results with this method?

1. In both languages I have wonderful passive skills. 

2. I can write in English without any translations in my head, but still make grammar mistakes and I usually avoid some grammar structures (rare tenses and conditionals).

3.In Hungarian I also can think without translation, but my thinking seem to be more restricted in comparison with English. My writing in Hungarian is «rendkívül furcsa» (extremely strange), because I usually write long sentences and use many words(my vocabulary is really nice), but make plenty of mistakes (in grammar, spelling and stylistics). 

Generally spoken, I think that you should find optimal strategy of language learning. You should do some grammar exercises, but don’t spend too much time with them. It's also important to note, that some languages probably require more serious approach to learning grammar (agglutinative languages like Hungarian).

No and yes. I don't believe in formal grammar and never have. What I learned in school, I forgot as fast as possible after it was no longer compulsory to study it. I don't like formal grammar at all and never study it the way it's usually taught in classes.

And yet, I do like learning languages. No grammar doesn't actually mean no grammar for me. I believe in patterns - the inherent underlying structure of a language, of how certain phrases and expressions always take the same forms, how certain words mutate depending on the situation. One can usually get that by sufficient repetitions.

That is how a child learns her mother tongue and how an illiterate adult native speaker can express himself perfectly well. I sidestep all formal grammar but I know the importance of patterns.

Caveat: I represent an unconventional minority. Most traditionalists will frown heavily on my strategy.

It depends...is it necessary to speak in coherent sentences?