Let's use "bank" as an example. Some Americans pronounce it /bæŋk/, using the vowel of TRAP. Others pronounce it /beŋk/, using the vowel of FACE.
Where are these two pronunciations found?
English Language & Usage Stack Exchange is a question and answer site for linguists, etymologists, and serious English language enthusiasts. It only takes a minute to sign up.Sign up to join this community
I think the pronunciation /beŋk/ is found all over the U.S. (although certainly lots of Americans say /bænk/). We have comments saying that it occurs in the Northeast, the South, the Upper Midwest, and the West. I know it's also found in the Midland accent (the lower Midwest). What proportion of speakers use it probably varies regionally, but I don't know if any studies have been done on this.
I also don't know how old this feature of the American accent is, but judging from how widespread it is, it must be fairly old.
See also this blog entry.
Wikipedia says it happens in California English, but I believe it's much more widespread in the U.S. than that.