I know the correct pronunciation (I think) of the words "ask" and "asked", but I quite often hear them pronounced as "ahks" and "ahksed" (almost like an "r" sound). I've heard it both in conversation and on television shows (both Australian and American).
Are these pronunciations due to dialect, or are they alternative pronunciations or incorrect pronunciations? If they are the correct pronunciation, should I use them or the "normal" pronunciation?
One of the earliest instances of the verb ask occurs in Old English as acsian. As the etymological note in the Oxford English Dictionary explains, acsian and axian survived down to nearly 1600 as the regular literary form, but was supplanted in Standard English by ask, originally the northern form.
As you have observed, a(h)ks is still heard in regional dialects. There is no doubt, however, that the standard form is ask, both in writing and in speech, and it is that form that foreign learners of English should use.
This is a sensitive argument, at least in the US.
As is noted, both pronunciations are ancient and were commonly mixed. In the US, for historical reasons, the /aks/ pronunciation was more commonly spoken in the south than the north, and the /ask/ more commonly spoken in the north. The pronunciation /aks/ has for the most part died among white speakers in the South, but is quite common among African-American speakers throughout the country (who migrated away from the south after the abolition of slavery).
In America, the African-American dialect is heavily stigmatized, and many otherwise racially conscious people, both white and black, will say quite ignorant and nasty things about it. In particular, some white Americans say /aks/ to make fun of the black dialect. Therefore, I strongly recommend that you not adopt it into your speech as a non-native speaker, as you will create serious problems if you are misinterpreted as doing this. Of course, if your accent is strong and you are obviously foreign, people will give you the benefit of the doubt, but it's ground I would not want to tread on. (If you are yourself black, you won't be misinterpreted as racist for saying /aks/ instead of /ask/, but racist people might make fun of you for it.)
This form of corruption of traditional pronunciation is a construct found in what are known as ghetto languages.
Though often seen as a substandard/subnormal level of English, there is some debate that these are learned dialects and are as valid as any regional or cultural patois.
However, if you are not of the culture or region, or very closely associated with it, you stand a large chance of coming across as either being condescending or offensive, so don't 'adopt' them if they're not part of your own circumstances. Also, due to ghetto language being mostly maligned (especially by conservative proponents), don't be surprised to find that people you speak to look down on its use.
