[Stevie Bain (OP)]

Benjamin would like to know:

Is it possible to see the same stars from anywhere in the world?

Can you help?

[evan_au]

Two nights ago I watched the familiar Southern Cross constellation drop below the horizon and disappear (apart from one of the pointer stars), as I flew from Australia into the Northern hemisphere.

The Southern Cross never sets from the viewpoint of my home in Sydney, but it dips below the horizon if you travel north of the equator. If you live in temperate parts of the Northern Hemisphere, you will never see it, because the bulk of the Earth is in the way.

Equally, I had never seen the (North) Pole Star until I travelled into the Northern Hemisphere.

So no, you can't see all the stars from most places in the world.
- But if you live on the equator, you will get to see all the stars at some time of the year - but the Pole Star will be right on the horizon, and very difficult to see.

[Janus]

Benjamin would like to know:

Is it possible to see the same stars from anywhere in the world?

Can you help?

No, you cannot. What stars you can see from any part of the world depends on your latitude (how far North or South of the equator you are)  For example, where I live, at ~45N latitude, I can never see Alpha Centauri.  If I were to take a trip to Hawaii, I would.    In Australia, I would be able to see the Southern Cross, but not the Big Dipper.   
At any given time  ~1/2 of the stars are above the horizon for any place on the Earth.  As the Earth rotates, different stars rise and set.  However, unless you are on the Equator, there will be some stars that will always be in the sky and never set. How large this part of the sky is depends on how far North or South you are from the Equator . At the North and South Poles, none of the stars in the sky ever rise or set, but just travel in a circle a fixed distance above the Horizon.  From anywhere on the equator, you could see any star at one time or another.

[evan_au]

I had never seen the (North) Pole Star until I travelled into the Northern Hemisphere

Last night I looked for Polaris from the hotel roof. It was above the horizon (as indicated by a smartphone app), but I was defeated by city lights and haze.

[chris]

I was defeated by city lights

So sad this; I only saw - and appreciated - the Milky Way properly for the first time in my life when I moved to Australia for a bit in my mid twenties. During one night in the outback I couldn't sleep for hours because I was so enthralled watching the star-scape. I had never understood what people were talking about before then. But the sad reality is - especially here in Europe - that light pollution is so extensive that we are missing one of Nature's most incredible spectacles...

Light pollution and efforts to reclaim the night were topics covered in an episode of Naked Astronomy earlier this year, if anyone is interested in following up.