In this funny clip, comedian Jimmy Carr demonstrates a common technique used for assuming an accent. He also makes the most of the opportunity to poke fun at Scousers (people from Liverpool).
As someone with a bit of a talent for accents myself, I have a few of my own phrases. They are useful because they encapsulate the things that make the accent distinctive. If you're not familiar with the accents I'm referring to here, this may be lost on you, but bear with me.
For example, for sounding like a Filipino, a phrase like "This burger has a nice flavour" is ideal, because it forces you to highlight the distinctive way Filipinos speak - heavy emphasis on the r sound, and f and v pronounced as p and b respectively.
For an Indonesian accent, the phrase I use is one that I heard while at a karaoke bar in Jakarta: "You are the sunshine of my life" (yes, it's the Stevie Wonder song). The r is rolled, the th becomes a d, "sunshine" becomes "sunsine", and "of" becomes either "off" or "op", according to your preference (a lot of Indonesians, like Filipinos, struggle with f and v).
For a Vietnamese accent, I like "This tastes very nice", which ends up sounding something like "This tay vey nai".
Know any other phrases that encapsulate a particular accent? Share them.