According to Biber et al.*, the verb "want" occurs in the progressive less than two percent of the time in the corpus of 40 million words of American and British English that they studied. They state:
"...verbs such as believe, know, like, and want are regarded as denoting mental states rather than processes [like hope, think, and wonder] and thus they rarely occur with the progressive..." (pp. 472-473).
Still, the progressive with the verb "want" is quite prevalent in English. For example "I've been wanting" occurs on Google 86, 400 times; "they've been wanting" 1,560 times; and "have you been wanting...?"4,240 times.
The progressive is used to emphasize the idea of duration: "I've been wanting" makes the wanting seem longer than "I've wanted." The progressive also makes the mental state more immediate and vivid than the perfect. This can be seen in Sentences 1 and 2 of Apple's examples.
Sentence 3 does not have enough context for an analysis, and Sentence 4 seems to be from Irish English, which uses the progressive much more than do British and American English. (the words "lads" for young men and "me" for "my" are typical of Irish English).
Here are a few examples from Google of how "want" is used in the progressive:
I've been wanting to create a testing setup, but have been putting it off "” my present machine can't handle that on top of design software.
. Lowe's was selling a mini-greenhouse kit with peat pods, and I've been wanting
to try growing an herb garden, so I picked up the kit along with some Basil
... He blamed police for the violence. ``They've been wanting to beat up on someone
all weekend and we haven't been giving them the excuse,'' Harold said.
Have you been wanting your own Web site but didn't know where to begin?
Have you been wanting to write your favorite screenwriter a letter, but just haven't been sure where to send it?
He hasn't been wanting to give up his company, but I don't see how he can
avoid it," says one of the fourth-round investors.
*Longman Grammar of Spoken and Written English (1999)