Do Japanese actually pronounce the "v" sound? They do have a kana character (ヴ) dedicated to transcribing foreign "v" sounds, but do they actually pronounce them like the English phoneme /v/ (using the upper teeth and the lower lip)? Or is it like a "weak" /b/ in Spanish, which is actually /β/ (using both lips)?
I think on reading ヴァ, ヴィ, etc., people usually try to pronounce it differently from バ, ビ, etc., but with varying success. In fact, I think most Japanese that try to distinguish ヴァ and バ pronounce what would be //v// indeed like the Spanish [[β]], a voiced bilabial fricative (or like a combination like [[bβ]]). That seems to make sense since the voiceless bilabial fricative [[ɸ]] is already present in Japanese (in フ [[ɸɯ]] and as ファ, フィ, etc. in loanwords).
I think one should point out, though, that while the katakana ヴ exists and is gaining ground, there is no particular standard of spelling words with ヴ and one will most often encounter the spelling with バ etc. and only rarely encounter the spelling with ヴ. Loanwords that were loaned a long time ago are usually much more resistant to respelling. For example, バージョン is rarely spelled ヴァージョン:
バージョン 1366 results
ヴァージョン 107 results
Major monolingual dictionaries, such as 大辞林, in fact still don't use ヴ at all and just note:
That is, ヴ is taken to be a particular katakana notation to indicate that a loanword was spelled with V. 大辞林 writes all loanwords containing V (e.g. ヴァージン, ヴィオラ, etc.) with バビブベボ (like バージン, ビオラ, etc.).
In any case, I think it can be said that the //v// phoneme doesn't (yet) exist in Japanese and for those speakers that do recognize it as different from //b//, it's almost never the voiced labiodental fricative [[v]], but rather the voiced bilabial fricative [[β]].
tl;dr: It varies, but it is usually a weak "b".
It varies from person to person, so some may pronounce it like the English "v", but others may use a strong "b" sound.
Originally, Japanese had no ヴ character so they used variations of ビ (bi). I think some Japanese might be able to do it, but they find it quite awkward. That's why television is called テレビ (terebi), it's hard for them to pronounce so they changed the sound. It's in the same vein as why they stick vowel sounds on the end of borrowed foreign words that end in constanants.
ヴ was probably introduced in order to reduce confusion and to retain accuracy when transliterating.