If you are attending a class that uses a course like Headway, English File or any other for that matter, the listening material generally uses speakers of British English. Not only British English, but a particular accent called "RP" - "received pronunciation". I'm not sure about the history of the name "received pronunciation" but it certainly isn't the most common accent in Britain - it reflects more a social class - that of the middle to upper class living in the Oxford/Cambridge/London triangle. For me, it reminds me of the BBC announcers from the thirties and forties. Who speaks like that these days?
Even more disturbing is the lack of material for American English. I don't know if it's different in the States, but the only courses that are based on American English I've seen are produced by Oxford University Press! Even if I don't like to admit it, American English is the English that dominates the international community.
The English phonemes that are given in the international Phonetic alphabet seem to based on received pronunciation too. I believe this because of the discussions I've had with American colleagues who pronounce a lot of sounds differently to me and agree that some of their sounds are not represented in the IPA.
Admittedly, Headway Intermediate does have a "guess my accent" exercise, where six people describe their capital city. As a native speaker, though, I can tell you that I couldn't recognise the Australian accent, the Irish speaker speaks so slowly it sounds nothing like the Irish people I know, the Scotsman has an incredibly posh Edinburgh accent that wouldn't be understood in Glasgow, and the Londoner has a RP accent that makes him sound more like Tony Blair than a "real" Londoner. I know that Cockney isn't the only London accent, but it would be worth using it in listening materials.
There is a good book for American English called "Great Ideas". Unfortunately it is 25 years old and sounds and looks a little dated. I use the cassette on its own just for listening practice.
Ask your students where they will be using their English skills and you will get a variety of answers. Among the people I'm currently working with, I hear the need to communicate in English with Arabs from the middle east, to attend meetings with Italian colleagues, to negotiate contract with Russians, in fact, just about every nationality except native British or Americans!
Have a look on the net for interviews in MP3 format that you can burn to CD and play to your students. If you can think of a famous person with an accent that your students will need to understand, you should be able to find something to download.
I'll do some research myself and post any useful links to the blog.