The answer to your question is that this is already possible.

Astronomers have been able to see hundreds of other galaxies apart from our own. The Hubble space telescope has produced some of the best images and revealed many different shapes of galaxies. You should check it out on the web at
hubblesite

Follow this link to see an image of many different galaxies taken from the Hubble. There are also lots of other good images on this site. To see other galaxies we must look away from the plane of our own galaxy with a very high resolution telescope. This is achieved by the Hubble as it is outside the earth's atmosphere (Fluctuations in the atmosphere cause a reduction in resolution for telescopes - this is called "seeing").

Other telescopes are often placed on high peaks away from external influences to try to improve resolution (e.g. the telescopes in Hawaii).

Scientists saw out of our galaxy with telescopes as early as the 1700's, though they did not realize it! Charles Messier (pronounced "Mess-see-YAY"), who lived during the French Revolution, made a catalog of "Messier objects." We now know that these objects included supernova remnants in our own galaxy (such as the Crab Nebula), open clusters in our own galaxy (such as the Pleidies), regions of star formation in our own galaxy (such as the Orion Nebula), globular clusters that orbit our galaxy, mostly around the central bulge (like M13, M12, M4, etc), and also other galaxies, spiral, elliptical, and irregular. One such galaxy is Andromeda; another is the Whirlpool galaxy (M51); yet another is called the Sombrero galaxy, because it looks like a hat.

In 1929 Edwin Hubble recognized a number of these other galaxies as moving away from us (and some toward us!). So, early in the last century scientists developed the capability to not only see outside our galaxy, but to make sensitive measurements of the light from other galaxies so as to be able to measure their motion. We now know that the entire universe is expanding!

Nowadays, with the Hubble Space Telescope and other very powerful ground-based scopes, we can see way back in time to the very first galaxies that ever formed, about 13 to 14 BILLION years ago, and 13 billion light years away, or more. (One light year is equivalent to the distance that light travels in one year in a vacuum, about 9 trillion kilometers.)

You can get more information about the images of Hubble Space Telescope from
hubble

Actually, you can see out of our galaxy with you own eyes. After about 10 pm look up in the sky towards the east -- you should notice a large blank area framed by 4 stars making a large nearly empty square. (This is the body of the horse in Pegasus). Where the "tail" comes off one corner (the north east corner as you view it), there are two rows of stars marching north, organized as east-west pairs that grow wider. (This is the constellation of Andromeda.)

If you look closely at the easterly "star" of the second pair, you should note that it is 'fuzzy'. Looking in binoculars, you will see a fuzzy spot which is the core of the Andromeda galaxy -- and the light that you see has been traveling toward earth for more than a million years. (In the southern hemisphere, the Magellanic Clouds are also galaxies in their own right.)

We did not know Andromeda was a galaxy until it was resolved into stars by the 100 inch Hooker telescope in about 1940. On the other hand, you can easily see the light of its billions of stars with your naked eyes,on any reasonably dark night.

Well, we already can see outside of the Milky Way galaxy. In fact you can ALSO see outside of the Milky Way galaxy!!if you find a star map (maybe on the web; or in the magazine SKY and TELESCOPE) you can determine where in the sky you need to look to see the faint fuzzy object called ANDROMEDA. This is another galaxy about 1.4 million light years away from Earth. All of the SINGLE stars you see at night are from the Milky Way galaxy, but you can see the light from other galaxies although you cannot make out individual stars.