This is a tricky one, RM. We already allow
brung, but that word is listed by a number of dictionaries as a dialect and/or non-standard alternative to
brought. However, the only dictionary I have seen that lists
brang is
Wiktionary, and that labels it as "nonstandard, illiterate", with a further usage note: "Generally used only to convey illiteracy of a particular character within prose."
Actually, from what I can see,
brang in dialogue is sometimes used to convey a regional pronunciation of
bring, perhaps similar to saying
thang for
thing.
However, the fact is that many people write
brang, at least in informal contexts, like online forums. This can be seen by typing phrases such as "brang it" or "brang up" into a search engine. While it appears that some of the people using this word are aiming for some humorous effect, many seem to be using it simply as their way of expressing the past tense of
bring.
Brang was used by Neil Diamond in his song
Play Me:
Song she sang to me
Song she brang to me
Words that rang in me
Rhyme that sprang from me
The
Satirium website reports that, after years of pressure from the National Association of Sticklers for the Precise Use of English, Neil Diamond admitted that he shouldn't have used the word
brang.
An interesting question is, if
brang is a dialect word, which dialects? It seems to be variously linked to Scotland, the north of England and the Ozarks. But the Australian Big Footy website has numerous uses of the word, perhaps more than of
brung. I'd guess that both
brang and
brung have arisen independently in many places, by analogy with
sing/sang/sung,
ring/rang/rung, etc, as suggested by the Neil Diamond lyrics.
To be completely logical, people saying
brang should use it only for the simple past tense (the preterite, as RM states) and use
brung for the past participle. So, just as you would say, "I rang the bell," but, "The bell was rung every evening," so you might say, "I brang you something," but, "See what I've brung you." However, people seem to use either
brang or
brung, but not both.
So, where does this leave us. The fact that a word appears in numerous places on the Internet is not conclusive, since any spelling mistake one can conceive of is present on multiple sites. And some of the passages where
brang is used are riddled with spelling and typing errors. But there are also examples where a piece of properly spelled and punctuated text contains the word, suggesting that it's a part of the writer's vocabulary.
It seems to me that
brang is pretty much in the same boat as
brung, although it may be that the latter is somewhat more widely used. So I think we should accept
brang, as we do
brung.