Why?
Don't confuse pronunciation with accent. Good pronunciation doesn't mean that we all have to talk like the Queen of England. As long as your pronunciation is understandable and pleasant that's fine, if people struggle to understand you then you may need to try and reduce your accent, but unless you are an actor, and you need to play different roles, or you want to become a spy, it's not worth trying to get rid of your accent.
That said, successful speaking is more than just knowing how to pronounce words correctly.
Enunciation is the act of speaking clearly and concisely, making each word sound as clear as possible, without sounding as if you think the person you are talking to is an idiot.
Elocution is about putting the right emphasis and nuance into what you are saying. Even kids born and bred in the UK take elocution lessons.
Tongue twisters are phrases or sentences that are designed to be difficult to say correctly. They are a great way of learning how to shape your mouth and position your tongue correctly. And best of all, they're fun!
Each tongue twister has its own page on Voice Thread, you can listen to my effort, and you can record your own efforts (if you're brave enough) - you'll need a Voice Thread account (as usual it's free) and a headset with a microphone.
