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But, besides that one, we also have another 'vibrating R', a uvular trill, represented phonetically by [ʀ], which is the 'rolled R' from some German dialects, for example. Chances are that this one is the one you've heard in Portugal, because, for untrained ears, it's very difficult to tell the difference between it and the alveolar one; both are passively produced trill consonants, but the former is made with the back of the tongue in the region of the uvula, while the latter is made with the tip of the tongue on the roof of the mouth. You can listen to and compare both of them here: https://en.wikipedia.org/wiki/Dental,_alveolar_and_postalveolar_trills and https://en.wikipedia.org/wiki/Uvular_trill

In Brazil, the uvular trill is quite common in German, French, or even Portuguese influenced communities. In Portugal, it is a common realization of that phoneme, probably because the standard European dialect favours uvular R's, so they've just kept the trill quality of the consonant, but moved the place of articulation (I mean, turning the ALVEOLAR trill into the UVULAR trill). But the uvular trill currently seems to be as common as the voiced uvular fricative ([ʁ]; the German or French R) in European Portuguese (or even a little less common) and probably occurs in free variation with it among many speakers (as it is the case in Brazil for people that produce the uvular trill).

In a nutshell, yes, both trilled R's are not standard in European (or Brazilian, for that matter) Portuguese anymore, but they're still fairly common in many dialects, nonetheless. Let me also refer you, Jack, to another answer I've given recently here exactly about all the possibilities for the R sound in Portuguese. It is a more thorough answer and it might interest and help you: https://www.italki.com/question/416366

Hope this helps!

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Good answers so far. Just disagreeing a little bit with Claudiano's answer, in the sense that the weak R is not vibrating at all—it's just a quick, active bounce against the roof of the mouth. That is exactly what makes it different from the rolled R, which is multiple bounces passively produced by vibration, and what makes both sounds phonemically different in some languages and dialects.

That said, you're right in your assumptions, Jack. When we say 'rolled R', we usually think of the Spanish one, that is [r], the alveolar trill. This one is not standard in Brazilian and European Portuguese anymore, but I think it is standard in some African dialects, for example. As you have presumed, though, it does happen in some local dialects, e.g., those influenced by Spanish, Arabic, or Italian communities here in Brazil, and also, yes, some conservative dialects in Portugal, in the North and rural areas (I think in Portugal it's not so much because of other languages' or communities' influences, but just a maintenance of this sound that once was Portuguese's standard strong R pronunciation as well).

Olá jack, boa tarde! Aqui no Brasil temos muitos sotaques, para mim, alguns são bem peculiares! Eu nasci na Bahia (nordeste brasileiro), mas já morei na cidade Goiânia (estado de Goiás) e agora resido em Brasília (Distrito Federal). Ou seja, já pude vivenciar alguns sotaques bem diferentes uns dos outros.

A pronúncia do R tem duas categorias: 1) Forte , 2) Fraco

1) R forte -> o som do R vem mais do fundo da garganta (mais gutural): Exemplos: roupa, rua, casar, comer, pregar, carro, correr

2) R fraco -> o som do R é influenciado pela ponta da lingua (que vibra para dar esse efeito "tremido" no som): Arara, Brasil, Prato. Em alguns casos esses "R" eles estão ao lado de outras consoantes, por isso esse som. Nesse caso, nos assemelhamos bastante aos hispanos.

Ademais, temos pessoas que pronunciam o R ao final das palavras (COMER, BEBER) com o som de R da palavra "NEVER", mas eu já escutei algumas pessoas pronunciando as mesmas palavras com a pronuncia do R semelhante aos hispanos. As palavras com RR tem um som mais forte, uma pronuncia mais marcada! CARRO, CORRER, CARREGAR. Eu acredito que em geral 

Por fim, não acredito que exista um padrão uniforme de sotaques na pronuncia do R aqui no Brasil, uma vez que os sotaques influenciam na pronuncia do R.

Se você quiser saber mais a respeito, veja esses vídeo: 

https://www.youtube.com/watch?v=IluDNBvbo6c

https://www.youtube.com/watch?v=AEwH-1CPTZM

It depends, you know we are a huge country, so in south or southeast of Brazil and part of center west (São Paulo - Minas gerais, not Rio de Janeiro or Espíruto Santo) we have influence of some german, italian, maily, but also poland ukrain  so the R's sound is well-marked in the midle of the word, but not in the begining, and just with one R, for exemple CARNE, PORTA.  But CARRO, RATO, RUÍNA, CARRAPATO is the same sound all of the country. The rest of our country when you listen the R in the midle it is less marked it is like you dont rolled but scratch the throat.

I hope it was understandable ;)